Question

a) Write T if the statement is true and F if the statement is false. 1) A relation R on a set A is called reflexive if (a, a) ? R for some element a ? A 2) A relation R on a set A is called antisymmetric if (b, a) ? R whenever (a, b) ? R, for all a, b ? A 3) The recurrence relation $a_n = 2a_{n-1} + a_{n-2}$ is linear homogeneous with constant coefficients (b) Identify the letter of the choice that best completes the statement or answers the question 1) One of the following is the contrapositive of $\sim r \rightarrow w$ a. $\sim w \rightarrow r$ b. $\sim r \rightarrow \sim w$ c. $w \rightarrow \sim r$ d. $r \rightarrow \sim w$ 2) One of the following is the negation of $\exists x \forall y \ p(x, y)$ a. $\exists x \forall y \ p(x, y)$ b. $\forall x \exists y \sim p(x, y)$ c. $\forall x \exists y \ p(x, y)$ d. $\forall y \exists x \ p(x, y)$ Final Assignment FALL 2023 3) If A is a set of 2 elements, then how many elements are in $A \times P(A \times P(A))$, where P is the power set. a. 7962624 b. 16777216 c. 512 d. 6561

          a) Write T if the statement is true and F if the statement is false.
1) A relation R on a set A is called reflexive if (a, a) ? R for some element a ? A
2) A relation R on a set A is called antisymmetric if (b, a) ? R whenever (a, b) ? R,
for all a, b ? A
3) The recurrence relation $a_n = 2a_{n-1} + a_{n-2}$ is linear homogeneous with constant coefficients
(b) Identify the letter of the choice that best completes the statement or answers the question
1) One of the following is the contrapositive of $\sim r \rightarrow w$
a. $\sim w \rightarrow r$
b. $\sim r \rightarrow \sim w$
c. $w \rightarrow \sim r$
d. $r \rightarrow \sim w$
2) One of the following is the negation of $\exists x \forall y \ p(x, y)$
a. $\exists x \forall y \ p(x, y)$
b. $\forall x \exists y \sim p(x, y)$
c. $\forall x \exists y \ p(x, y)$
d. $\forall y \exists x \ p(x, y)$
Final Assignment
FALL 2023
3) If A is a set of 2 elements, then how many elements are in $A \times P(A \times P(A))$, where P is the power set.
a. 7962624
b. 16777216
c. 512
d. 6561

a) Write T if the statement is true and F if the statement is false.
1) A relation R on a set A is called reflexive if (a, a) ? R for some element a ? A
2) A relation R on a set A is called antisymmetric if (b, a) ? R whenever (a, b) ? R,
for all a, b ? A
3) The recurrence relation an = 2an-1 + an-2 is linear homogeneous with constant coefficients
(b) Identify the letter of the choice that best completes the statement or answers the question
1) One of the following is the contrapositive of ∼ r → w
a. ∼ w → r
b. ∼ r →∼ w
c. w →∼ r
d. r →∼ w
2) One of the following is the negation of ∃ x ∀ y p(x, y)
a. ∃ x ∀ y p(x, y)
b. ∀ x ∃ y ∼ p(x, y)
c. ∀ x ∃ y p(x, y)
d. ∀ y ∃ x p(x, y)
Final Assignment
FALL 2023
3) If A is a set of 2 elements, then how many elements are in A × P(A × P(A)), where P is the power set.
a. 7962624
b. 16777216
c. 512
d. 6561

Added by Lorenzo G.

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