Question

Tautology: a statement that is always true, no matter what. If you construct a truth table for a statement and all of the column values for the statement are true (T), then the statement is a tautology because it's always true! For #s 1-3, determine if the given compound statement is a tautology. Ex 1: $[p \land (p \to q)] \to q$ Condition condition and P q $p \to q$ $p \land ()$ $ \to q$ T T T F T T T F F F T F F F T F Ex 2: $(p \to q) \land (\neg q \to \neg p)$ P q $p \to q$ $\neg p \to \neg q$ T T T T T F F F T T F F T Ex 3: $(q \to p) \lor (\neg p \to \neg q)$ P q $q \to p$ T T T T F T F T F F T

          Tautology: a statement that is always true, no matter what. If you construct a truth table for a
statement and all of the column values for the statement are true (T), then the statement is a tautology
because it's always true!
For #s 1-3, determine if the given compound statement is a tautology.
Ex 1: $[p \land (p \to q)] \to q$
Condition
condition
and
P
q
$p \to q$
$p \land ()$ 
$ \to q$
T
T
T
F
T
T
T
F
F
F
T
F
F
F
T
F
Ex 2: $(p \to q) \land (\neg q \to \neg p)$
P
q
$p \to q$
$\neg p \to \neg q$
T
T
T
T
T
F
F
F
T
T
F
F
T
Ex 3: $(q \to p) \lor (\neg p \to \neg q)$
P
q
$q \to p$
T
T
T
T
F
T
F
T
F
F
T

Show more…

Tautology: a statement that is always true, no matter what. If you construct a truth table for a
statement and all of the column values for the statement are true (T), then the statement is a tautology
because it's always true!
For #s 1-3, determine if the given compound statement is a tautology.
Ex 1: [p (p → q)] → q
Condition
condition
and
P
q
p → q
p ()
→ q
T
T
T
F
T
T
T
F
F
F
T
F
F
F
T
F
Ex 2: (p → q) ( q → p)
P
q
p → q
p → q
T
T
T
T
T
F
F
F
T
T
F
F
T
Ex 3: (q → p) ( p → q)
P
q
q → p
T
T
T
T
F
T
F
T
F
F
T

Added by Eduardo H.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Bradley Duda

Step 1

| P | Q | P∧(P ∨ Q) | [P∧(P ∨ Q)] → Q | |---|---|-----------|-----------------| | T | T | T | T | | T | F | T | F | | F | T | F | T | | F | F | F | T | As we can see from the Show more…

Show all steps

lock

Thanks for your feedback!

Tautology: a statement that is always true; no matter what. If you construct a truth table for a statement and all of the column values for the statement are true (T), then the statement is a 'tautology' because it's always true. For #5 1-3, determine if the given compound statement is a tautology: Ex 1: [Pâˆ§(P âˆ¨ Q)] â†’ Q Ex 2: (P â†’ Q) âˆ§ (Â¬Q â†’ Â¬P) Ex 3: (Q âˆ¨ P) âˆ¨ (Â¬P âˆ§ Q)

Play audio

Feedback

Powered by NumerAI

Bradley Duda and 74 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later