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The IIT Foundation series of Mathematics Class

Trishna Knowledge Systems

Chapter 5

Statements - all with Video Answers

Educators

Chapter Questions

01:29

Problem 1

For which of the following cases does the statement $\mathrm{p} \wedge \sim \mathrm{q}$ take the truth value as true?
(1) $\mathrm{p}$ is true, $\mathrm{q}$ is true
(2) $\mathrm{p}$ is false, $\mathrm{q}$ is true
(3) $\mathrm{p}$ is false, $\mathrm{q}$ is false
(4) $\mathrm{p}$ is true, $\mathrm{q}$ is false

Abhijith V
Abhijith V
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01:55

Problem 2

Which of the following sentences is a statement?
(1) Ramu is a clever boy
(2) What are you doing?
(3) Oh! It is amazing
(4) Two is an odd number.

Abhijith V
Abhijith V
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01:49

Problem 3

Which of the following laws does the connective $\wedge$ satisfy?
(1) Commutative law
(2) Idempotent law
(3) Associative law
(4) All the above

Abhijith V
Abhijith V
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01:02

Problem 4

The truth value of the statement, "We celebrate our Independence day on August 15 th", is
(1) $\overline{\mathrm{T}}$
(2) $\mathrm{F}$
(3) neither T nor $\mathrm{F}$
(4) Cannot be determined

Abhijith V
Abhijith V
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02:20

Problem 5

When does the inverse of the statement $\sim \mathrm{p} \Rightarrow \mathrm{q}$ results in $\mathrm{T}$ ?
(1) $\mathrm{p}=\mathrm{T}, \mathrm{q}=\mathrm{T}$
(2) $\mathrm{p}=\mathrm{T}, \mathrm{q}=\mathrm{F}$
(3) $\mathrm{p}=\mathrm{F}, \mathrm{q}=\mathrm{F}$
(4) Both (2) and (3).

Abhijith V
Abhijith V
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01:57

Problem 6

Which of the following is a contradiction?
(1) $\mathrm{p} \vee \mathrm{q}$
(2) $\mathrm{p} \wedge \mathrm{q}$
(3) $\mathrm{p} \vee \sim \mathrm{p}$
(4) $\mathrm{p} \wedge \sim \mathrm{p}$

Abhijith V
Abhijith V
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01:30

Problem 7

In which of the following cases, $\mathrm{p} \Leftrightarrow \mathrm{q}$ is true?
(1) $\mathrm{p}$ is true, $\mathrm{q}$ is true
(2) $\mathrm{p}$ is false, $\mathrm{q}$ is true
(3) $\mathrm{p}$ is true, $\mathrm{q}$ is false
(4) None of these

Abhijith V
Abhijith V
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01:17

Problem 8

Find the counter example of the statement "Every natural number is either prime or composite".
(1) 5
(2) 1
(3) 6
(4) None of these

Abhijith V
Abhijith V
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01:52

Problem 9

Which of the following pairs are logically equivalent?
(1) Conditional, Contrapositive
(2) Conditional, Inverse
(3) Contrapositive, Converse
(4) Inverse, Contrapositive

Abhijith V
Abhijith V
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01:02

Problem 10

The property $\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r}) \equiv(\mathrm{p} \wedge \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{r})$ is called
(1) associative law
(2) commutative law
(3) distributive law
(4) idempotent law

Abhijith V
Abhijith V
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02:09

Problem 11

Which of the following is contingency?
(1) $\mathrm{P} \vee \sim \mathrm{p}$
(2) $\mathrm{p} \wedge \mathrm{q} \Rightarrow \mathrm{p} \vee \mathrm{q}$
(3) $\mathrm{p} \wedge(\sim \mathrm{q})$
(4) None of these

Abhijith V
Abhijith V
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02:08

Problem 12

Which of the following pairs are logically equivalent?
(1) Converse, Contrapositive
(2) Conditional, Converse
(3) Converse, Inverse
(4) Conditional, Inverse

Abhijith V
Abhijith V
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03:21

Problem 13

Which of the following connectives can be used for describing a switching network?
(1) $(\mathrm{p} \wedge \mathrm{q}) \vee \mathrm{p}^{\prime}$.
(2) $(\mathrm{p} \vee \mathrm{q}) \wedge \mathrm{q}^{\prime}$
(3) Both
(1) and (2).
(4) None of these

Abhijith V
Abhijith V
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01:34

Problem 14

Find the quantifier which best describes the variable of the open sentence $\mathrm{x}+3=5$.
(1) Universal
(2) Existential
(3) Neither (1) nor (2)
(4) Cannot be determined

Abhijith V
Abhijith V
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02:34

Problem 15

Which of the following is equivalent to $p \Leftrightarrow q$ ?
(1) $\mathrm{p} \Rightarrow \mathrm{q}$
(2) $\mathrm{q} \Rightarrow \mathrm{p}$
(3) $(\mathrm{p} \Rightarrow \mathrm{q}) \wedge(\mathrm{q} \Rightarrow \mathrm{p})$
(4) None of these

Abhijith V
Abhijith V
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01:34

Problem 16

The property $\sim(\mathrm{p} \wedge \mathrm{q}) \equiv \sim \mathrm{p} \vee \sim \mathrm{q}$ is called
(1) associative law
(2) De morgan's law
(3) commutative law
(4) idempotent law

Abhijith V
Abhijith V
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01:29

Problem 17

The statement $\mathrm{p} \vee \mathrm{q}$ is
(1) a tautology
(2) a contradiction
(3) neither a tautology nor a contradiction
(4) Cannot say

Abhijith V
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01:53

Problem 18

Which of the following compound statement represents a series network?
(1) $\mathrm{p} \vee \mathrm{q}$
(2) $\mathrm{p} \Rightarrow \mathrm{q}$
(3) $\mathrm{p} \wedge \mathrm{q}$
(4) $\mathrm{p} \Leftrightarrow \mathrm{q}$

Abhijith V
Abhijith V
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01:55

Problem 19

Which of the following is a tautology?
(1) $\mathrm{p} \wedge \mathrm{q}$
(2) $\mathrm{p} \vee \mathrm{q}$
(3) $\mathrm{P} \vee \sim \mathrm{p}$
(4) $\mathrm{p} \wedge \sim \mathrm{p}$

Abhijith V
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01:35

Problem 20

Find the truth value of the compound statement, 'If 2 is a prime number, then hockey is the national game of India'.
(1) $\mathrm{T}$
(2) E
(3) Neither T nor E
(4) Cannot be determined

Abhijith V
Abhijith V
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01:05

Problem 21

Find the truth value of the compound statement, 4 is the first composite number and $2+5=7$.
(1) $\mathrm{T}$
(2) $\mathrm{F}$
(3) Neither T nor $\mathrm{F}$
(4) Cannot be determined

Abhijith V
Abhijith V
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01:16

Problem 22

Find the inverse of the statement, "If $\Delta \mathrm{ABC}$ is equilateral, then it is isosceles".
(1) If $\triangle \mathrm{ABC}$ is isosceles, then it is equilateral.
(2) If $\triangle \mathrm{ABC}$ is not equilateral, then it is isosceles.
(3) If $\triangle \mathrm{ABC}$ is not equilateral, then it is not isosceles.
(4) If $\triangle \mathrm{ABC}$ is not isosceles, then it is not equilateral.

Abhijith V
Abhijith V
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01:25

Problem 23

The statement $\mathrm{p} \Rightarrow \mathrm{p} \vee \mathrm{q}$ is
(1) a tautology
(2) a contradiction
(3) both tautology and contradiction
(4) neither a tautology nor a contradiction

Abhijith V
Abhijith V
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01:25

Problem 23

The statement $\mathrm{p} \Rightarrow \mathrm{p} \vee \mathrm{q}$ is
(1) a tautology
(2) a contradiction
(3) both tautology and contradiction
(4) neither a tautology nor a contradiction

Abhijith V
Abhijith V
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01:30

Problem 24

What is the truth value of the statement 'Two is an odd number iff 2 is a root of $x^{2}+2=0^{\prime}$ ?
(1) $\mathrm{T}$
(2) $\mathrm{F}$
(3) Neither T nor F
(4) Cannot be determined

Abhijith V
Abhijith V
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01:54

Problem 25

Which of the following connectives satisfy commutative law?
(1)
(2) $\vee$
(3) $\Leftrightarrow$
(4) All the above

Abhijith V
Abhijith V
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02:39

Problem 26

$\sim[\sim p \wedge(p \Leftrightarrow q)] \equiv$
(1) $\mathrm{p} \vee \mathrm{q}$
(2) $\mathrm{q} \wedge \mathrm{p}$
(3) $\mathrm{T}$
(4) $\mathrm{F}$

Abhijith V
Abhijith V
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01:20

Problem 27

Write the negation of the statement "If the switch is on, then the fan rotates".
(1) "If the switch is not on, then the fan does not rotate".
(2) "If the fan does not rotate, then the switch is not on".
(3) "The switch is not on or the fan rotates".
(4) "The switch is on and the fan does not rotate".

Abhijith V
Abhijith V
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02:57

Problem 28

If $\mathrm{p}:$ The number of factors of 20 is 5 and $\mathrm{q}: 2$ is an even prime number, then the truth values of inverse and contrapositive of $\mathrm{p} \Rightarrow \mathrm{q}$ respectively are
(1) $\mathrm{T}, \mathrm{T}$
(2) $\mathrm{F}, \mathrm{F}$
(3) $\mathrm{T}, \mathrm{F}$
(4) $\mathrm{F}, \mathrm{T}$

Abhijith V
Abhijith V
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01:33

Problem 29

"No square of a real number is less than zero" is equivalent to
(1) for every real number a, a is non-negative.
(2) $\forall \mathrm{a} \in \mathrm{R}, \mathrm{a}^{2} \geq 0$
(3) either (1) or (2)
(4) None of these

Abhijith V
Abhijith V
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02:40

Problem 30

If a compound statement $\mathrm{r}$ is contradiction, then find the truth value of $(p \Rightarrow q) \wedge(r) \wedge[p \Rightarrow(\sim r)]$
(1) $\mathrm{T}$
(2) F
(3) $\mathrm{T}$ or $\mathrm{F}$
(4) None of these

Abhijith V
Abhijith V
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02:11

Problem 31

Which of the following is/are counter example(s) of the statement $\mathrm{x}^{2}-7 \mathrm{x}+10>0$, for all real $\mathrm{x}$ ?
(a) 2
(b) 3
(c) 4
(d) 5
(1) Only (a) and (d)
(2) Only (b) and (c)
(3) All (a), (b), (c) and (d)
(4) None of these

Abhijith V
Abhijith V
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03:08

Problem 32

If $\mathrm{p}: 3$ is an odd number and q: 15 is a prime number, then the truth value of $[\sim(\mathrm{p} \Leftrightarrow \mathrm{q})]$ is equivalent to that of
$\begin{array}{llll}\text { (a) } p \Leftrightarrow(\sim q) & \text { (b) }(\sim p) \Leftrightarrow q & (c) \sim(p \wedge q)\end{array}$
(1) only (a)
(2) only (c)
(3) Both
(a) and
(b)
(4) (a), (b) and (c)

Abhijith V
Abhijith V
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02:17

Problem 33

The compound statement, "If you want to top the school, then you do not study hard" is equivalent to
(1) "If you want to top the school, then you need to study hard".
(2) "If you will not top in the school, then you study hard".
(3) "If you study hard, then you will not top the school".
(4) "If you do not study hard, then you will top in the school".

Abhijith V
Abhijith V
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02:43

Problem 34

If $\mathrm{p}: 25$ is a factor of 625 and q: 169 is a perfect square then $\sim(\mathrm{p} \Rightarrow \mathrm{q})$ is equivalent to
(1) $\mathrm{p} \wedge \mathrm{q}$
(2) $(\sim p) \wedge q$
(3) $\mathrm{p} \wedge(\sim \mathrm{q})$
(4) Both (2) and (3)

Abhijith V
Abhijith V
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01:40

Problem 35

The compound statement, "If you won the race, then you did not run faster than others" is equivalent to
(1) "If you won the race, then you ran faster than others".
(2) "If you ran faster than others, then you won the race".
(3) "If you did not win the race, then you did not run faster than others".
(4) "If you ran faster than others, then you did not win the race".

Abhijith V
Abhijith V
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01:29

Problem 36

"If $\mathrm{x}$ is a good actor, then $\mathrm{y}$ is bad actress" is
(1) a tautology
(2) a contradiction
(3) a contingency
(4) None of these

Abhijith V
Abhijith V
Numerade Educator
01:29

Problem 37

Which of the following is negation of the statement "All birds can fly".
(1) "Some birds cannot fly".
(2) "All the birds cannot fly".
(3) "There is at least one bird which can fly"
(4) All the above.

Abhijith V
Abhijith V
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01:36

Problem 38

What are the truth values of $(\sim \mathrm{p} \Rightarrow \sim \mathrm{q})$ and $\sim(\sim \mathrm{p} \Rightarrow \mathrm{q})$ respectively, when $\mathrm{p}$ and $\mathrm{q}$ always speak true in any argument?
(1) $\mathrm{T}, \mathrm{T}$
(2) $\mathrm{F}, \mathrm{F}$
(3) $\mathrm{T}, \mathrm{F}$
(4) $\mathrm{F}, \mathrm{T}$

Abhijith V
Abhijith V
Numerade Educator
02:20

Problem 39

If $\mathrm{p}: 4$ is an odd number and $\mathrm{q}: 4^{3}$ is an even number, then which of the following is equivalent to $\sim(\mathrm{p} \Rightarrow \mathrm{q})$ ?
(1) " 4 is an odd number and $4^{3}$ is an even number".
(2) "The negation of the statement " 4 is not an odd number or $4^{3}$ is not an even number".
(3) Both (1) and (2)
(4) None of these

Abhijith V
Abhijith V
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01:14

Problem 40

In the above network, current flows from $\mathrm{N}$ to $\mathrm{T}$ when
(1) p closed, q closed, ropened and s opened.
(2) p closed, q opened, s closed and r opened.
(3) q closed, p opened, $\mathrm{r}$ opened and s closed.
(4) p opened, q opened, $\mathrm{r}$ closed and s closed.

Abhijith V
Abhijith V
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03:30

Problem 41

If $\mathrm{p}:$ In a triangle, the centroid divides each median in the ratio $1: 2$ from the vertex and $\mathrm{q}: \mathrm{In}$ an equilateral triangle, each median is perpendicular bisector of one of its sides. The truth values of inverse and converse of $\mathrm{p} \Rightarrow \mathrm{q}$ are respectively
(1) $\mathrm{T}, \mathrm{T}$
(2) $\mathrm{F}, \mathrm{F}$
(3) $\mathrm{T}, \mathrm{F}$
(4) $\mathrm{F}, \mathrm{T}$

Abhijith V
Abhijith V
Numerade Educator
01:43

Problem 42

If $\mathrm{p}$ always speaks against $\mathrm{q}$, then $\mathrm{p} \Rightarrow \mathrm{p} \vee \sim \mathrm{q}$ is
(1) a tautology
(2) contradiction
(3) contingency
(4) None of these

Abhijith V
Abhijith V
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01:55

Problem 43

If p: Every equilateral triangle is isosceles and q: Every square is a rectangle, then which of the following is equivalent to $\sim(p \Rightarrow q)$ ?
(1) The negation of "Every equilateral triangle is not isosceles or every square is rectangle".
(2) "Every equilateral triangle is not isosceles, then every square is not a rectangle".
(3) "Every equilateral triangle is isosceles, then every square is a rectangle".
(4) None of these

Abhijith V
Abhijith V
Numerade Educator
02:25

Problem 44

When does the value of the statement $(\mathrm{p} \wedge \mathrm{r}) \Leftrightarrow(\mathrm{r} \wedge \mathrm{q})$ become false?
(1) $\mathrm{p}$ is $\mathrm{T}, \mathrm{q}$ is $\mathrm{F}$
(2) $\mathrm{p}$ is $\mathrm{F}, \mathrm{r}$ is $\mathrm{F}$
(3) $\mathrm{p}$ is $\mathrm{F}, \mathrm{q}$ is $\mathrm{F}$ and $\mathrm{r}$ is $\mathrm{F}$
(4) None of these

Abhijith V
Abhijith V
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01:37

Problem 45

If the truth value of $\mathrm{p} \vee \mathrm{q}$ is true, then truth value $\sim \mathrm{p} \wedge \mathrm{q}$ is
(1) false if $\mathrm{p}$ is true
(2) true if $\mathrm{p}$ is true
(3) false if $q$ is true
(4) true if $\mathrm{q}$ is true

Abhijith V
Abhijith V
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02:32

Problem 46

The compound statement, "If you want to win the gold medal in Olympics, then you need to work hard" is equivalent to
(1) "If you will not win the gold medal in Olympics, then you need not work hard."
(2) "If you do not work hard, then you will not win the gold medal in Olympics."
(3) Both (1) and (2)
(4) None of these

Abhijith V
Abhijith V
Numerade Educator
02:31

Problem 47

If p: sum of the angles in a triangle is $180^{\circ}$ and q: every angle in a triangle is more than $0^{\circ}$, then $(p \Rightarrow q) \vee p$ is equivalent to
(1) $\mathrm{p} \vee \sim \mathrm{q}$
(2) $(p \wedge q) \Rightarrow p$
(3) $\sim \mathrm{p} \wedge \sim \mathrm{q}$
(4) Both (1) and (2)

Abhijith V
Abhijith V
Numerade Educator
01:50

Problem 48

Which of the following is the negation of the statement, "All animals are carnivores"?
(1) Some animals are not carnivores.
(2) Not all animals are carnivores.
(3) There is atleast one animal which is not carnivores.
(4) All the above.

Abhijith V
Abhijith V
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02:06

Problem 49

$(\mathrm{p} \Leftrightarrow \mathrm{q}) \Leftrightarrow(\sim \mathrm{p} \Leftrightarrow \sim \mathrm{q})$ is a
(1) tautology
(2) contradiction
(3) contingency
(4) None of these

Abhijith V
Abhijith V
Numerade Educator
01:25

Problem 50

Which of the following is a counter example of $x^{2}-6 x+8 \leq 0$ ?
(1) $\mathrm{x}=2$
(2) $x=3$
(3) $\mathrm{x}=4$
(4) $\mathrm{x}=5$

Abhijith V
Abhijith V
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02:10

Problem 51

If $\mathrm{p}$ and $\mathrm{q}$ are two statements, then $\mathrm{p} \vee \sim(\mathrm{p} \Rightarrow \sim \mathrm{q})$ is equivalent to
(1) $\mathrm{p} \wedge \sim \mathrm{q}$
(2) $\mathrm{p}$
(3) q
$(4) \sim \mathrm{p} \wedge \mathrm{q}$

Abhijith V
Abhijith V
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01:57

Problem 52

In the above network, current does not flow, when
(1) p opened, q opened and $\mathrm{r}$ opened.
(2) p closed, q opened and $r$ opened.
(3) p opened, q closed and $r$ closed.
(4) None of these

Abhijith V
Abhijith V
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01:31

Problem 53

The contropositive of the statement $\sim \mathrm{p} \Rightarrow(\mathrm{p} \wedge \sim \mathrm{q})$ is
(1) $\mathrm{p} \Rightarrow(\sim \mathrm{p} \vee \mathrm{q})$
(2) $\mathrm{p} \Rightarrow(\mathrm{p} \wedge \mathrm{q})$
(3) $\mathrm{p} \Rightarrow(\sim \mathrm{p} \wedge \mathrm{q})$
(4) $(\sim p \vee q) \Rightarrow p$

Abhijith V
Abhijith V
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02:20

Problem 54

In the above circuit, the current flows from $A$ to $B$ when
(1) $\mathrm{p}$ is closed, $\mathrm{q}$ is open $\mathrm{r}$ is open.
(2) $\mathrm{p}$ is closed, $\mathrm{q}$ is closed and $\mathrm{r}$ is open.
(3) $\mathrm{p}$ is closed, $\mathrm{q}$ is closed and $\mathrm{r}$ is closed.
(4) all the above

Abhijith V
Abhijith V
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02:02

Problem 55

If $\mathrm{p}: 5 \mathrm{x}+6=8$ is an open sentence and $\mathrm{q}: 3,4$ are the roots of the equation $\mathrm{x}^{2}-7 \mathrm{x}+12=0$, then which of following is equivalent to $\sim[\sim \mathrm{p} \vee \mathrm{q}]$ ?
(1) "The negation of "If $5 \mathrm{x}+6=8$ is an open sentence, then 3,4 are the roots of the equation $\mathrm{x}^{2}-7 \mathrm{x}+$ $12=0 "$
(2) $5 \mathrm{x}+6=8$ is an open sentence or 3,4 are not roots of the equation $\mathrm{x}^{2}-7 \mathrm{x}+12=0$
(3) $5 \mathrm{x}+6=8$ is not an open sentence and 3,4 are the roots of the equation $\mathrm{x}^{2}-7 \mathrm{x}+12=0$
(4) None of these

Abhijith V
Abhijith V
Numerade Educator
01:25

Problem 56

If the truth value of $\mathrm{p} \mathrm{V} \mathrm{q}$ is $\mathrm{T}$, then the truth value $\mathrm{p} \wedge \mathrm{q}$ is
(1) $\mathrm{T}$
(2) $\mathrm{F}$
(3) neither $\mathrm{T}$ or $\mathrm{F}$
(4) Cannot be determined

Abhijith V
Abhijith V
Numerade Educator
01:01

Problem 57

$(p \vee \sim q) \wedge q$ is equivalent to
(1) $\mathrm{p} \vee \mathrm{q}$
(2) $\mathrm{p} \wedge \mathrm{q}$
(3) $\mathrm{p} \vee \sim \mathrm{q}$
(4) $\mathrm{p} \wedge \sim \mathrm{q}$

Abhijith V
Abhijith V
Numerade Educator
01:42

Problem 58

Which of the following is a tautology?
(1) $\mathrm{p} \Rightarrow(\mathrm{q} \vee \sim \mathrm{q})$
(2) $p \Leftrightarrow(\sim q \wedge p)$
(3) $p \Leftrightarrow(p \wedge \sim p)$
(4) $(\mathrm{p} \wedge \sim \mathrm{p}) \wedge \mathrm{q}$

Abhijith V
Abhijith V
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02:10

Problem 59

$\sim[\sim p \vee(\sim p \Leftrightarrow q)]$ is equivalent to
(1) $\mathrm{p} \wedge(\mathrm{p} \Leftrightarrow \mathrm{q})$
(2) $\mathrm{p} \wedge \mathrm{q}$
(3) Both
(1) and (2)
(4) None of these

Abhijith V
Abhijith V
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01:12

Problem 60

When does the truth value of the statement $(\mathrm{p} \Rightarrow \mathrm{q}) \vee(\mathrm{r} \Leftrightarrow \mathrm{s})$ become true?
(1) $\mathrm{p}$ is true
(2) $\mathrm{q}$ is true
(3) $\mathrm{r}$ is true
(4) $s$ is true

Abhijith V
Abhijith V
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01:23

Problem 61

Given that $\mathrm{p}: \mathrm{x}$ is a prime number and $\mathrm{q}: \mathrm{x}^{2}$ is a composite number. Then $\sim(\sim \mathrm{p} \Rightarrow \mathrm{q})$ is equivalent to
(1) $\mathrm{x}$ is not a prime number and $\mathrm{x}^{2}$ is not a composite number
(2) $\mathrm{x}$ is not a prime number and $\mathrm{x}^{2}$ is a composite number
(3) Both (1) and (2)
(4) None of these

Abhijith V
Abhijith V
Numerade Educator
02:10

Problem 62

Which of the following is a contradiction?
(1) $(\mathrm{p} \vee \mathrm{q}) \Leftrightarrow(\mathrm{p} \wedge \mathrm{q})$
(2) $(\mathrm{p} \vee \mathrm{q}) \Rightarrow(\mathrm{p} \wedge \mathrm{q})$
(3) $(p \Rightarrow q) \vee(q \Rightarrow p)$
$(4)(\sim q) \wedge(p \wedge q)$

Abhijith V
Abhijith V
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01:29

Problem 63

When does the truth value of the statement $[(p \Leftrightarrow q) \Rightarrow(q \Leftrightarrow r)] \Rightarrow(r \Leftrightarrow p)$ become false?
(1) $\mathrm{p}$ is true, $\mathrm{q}$ is false, $\mathrm{r}$ is true
(2) $\mathrm{p}$ is false, $\mathrm{q}$ is true, $\mathrm{r}$ is true
(3) $\mathrm{p}$ is false $\mathrm{q}$ is false, $\mathrm{r}$ is false
(4) $\mathrm{p}$ is true, $\mathrm{q}$ is true, $\mathrm{r}$ is true

Abhijith V
Abhijith V
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01:25

Problem 64

If $\mathrm{p}$ is negation of $\mathrm{q}$, then $(\mathrm{p} \Rightarrow \mathrm{q}) \vee(\mathrm{q} \Rightarrow \mathrm{p})$ is $\mathrm{a}$
(1) tautology
(2) contradiction
(3) contingency
(4) none of these

Abhijith V
Abhijith V
Numerade Educator
02:09

Problem 65

Which of the following is a contingency?
(1) $\sim \mathrm{p} \wedge \mathrm{q}$
(2) $\mathrm{p} \vee \sim \mathrm{q}$
(3) $\sim$ p $\wedge \sim$ q
(4) All of these

Abhijith V
Abhijith V
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01:07

Problem 66

Which among the following is negation of $\sim(\mathrm{p} \wedge \mathrm{q}) \vee \mathrm{r}$ ?
(1) $(p \wedge q) \vee r$
(2) $(\mathrm{p} \vee \mathrm{q}) \vee \sim \mathrm{r}$
(3) $(\mathrm{p} \vee \mathrm{q}) \vee \mathrm{r}$
(4) $(p \wedge q) \wedge \sim r$

Abhijith V
Abhijith V
Numerade Educator
01:44

Problem 67

The inverse of a conditional statement is, "If $\mathrm{ABC}$ is a triangle, then $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^{\circ}$ ". Then the contrapositive of the conditional statement is
(1) "If $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^{\circ}$, then $\mathrm{ABC}$ is a triangle.
(2) "If $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C} \neq 0$, then $\mathrm{ABC}$ is not a triangle.
(3) "If $\mathrm{ABC}$ is not a triangle, then $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C} \neq 180^{\circ}$.
(4) "If $\mathrm{ABC}$ is a triangle, then $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^{\circ}$.

Abhijith V
Abhijith V
Numerade Educator
01:24

Problem 68

"There is atleast one prime number which is not odd number". The quantifier used in the above statement is
(1) Universal quantifier
(2) Existential quantifier
(3) both (1) and (2)
(4) no quantifier used

Abhijith V
Abhijith V
Numerade Educator
01:38

Problem 69

In the above network, current flows from $\mathrm{M}$ to $\mathrm{N}$, when
(1) p closed, q closed
(2) p closed, q opened
(3) p opened, q closed
(4) p opened, q opened

Abhijith V
Abhijith V
Numerade Educator
01:07

Problem 70

In the above network, current flows from $A$ to $B$, when
(1) p opened, q opened.
(2) $\mathrm{p}$ closed, q closed.
(3) p closed, q opened.
(4) $\mathrm{p}$ opened, q closed.

Abhijith V
Abhijith V
Numerade Educator