Question 22 Consider the following statement: ∀x  Z, [(2x + 4 > 0)  (4 - x 2 ≤ 0)] The negation of the above statement is: ¬[∀x  Z, [(2x + 4 > 0)  (4 - x 2 ≤ 0)]] ≡ ∃x  Z, ¬[(2x + 4 > 0)  (4 - x 2 ≤ 0)] ≡ ∃x  Z, [¬(2x + 4 > 0) ∧ ¬(4 - x 2 ≤ 0)] ≡ ∃x  Z, [(2x + 4 ≤ 0) ∧ (4 - x 2 > 0)] 1. True 2. False Question 23 Consider the statement If n is even, then 4n2 - 3 is odd. The contrapositive of the given statement is: If 4n2 - 3 is odd, then n is even. 1. True 2. False

Question 22

Let us consider the statement $∀x \in\Z, [(2x + 4 > 0) \lor(4 - x^2 ≤ 0)]$

The negation of the above statement is:

$\neg[∀x \in\Z, [(2x + 4 > 0) \lor(4 - x^2 ≤ 0)]]≡ \exists x \in\Z, \neg[(2x + 4 > 0) \lor(4 - x^2 ≤ 0)]≡ \exists x \in\Z, [\neg(2x + 4 > 0) \land\neg(4 - x^2 ≤ 0)]≡ \exists x \in\Z, [(2x + 4 \le 0) \land(4 - x^2 >0)]$

Answer: 1. True

Question 23

Let us consider the statement "If $n$ is even, then $4n^2- 3$ is odd". The contrapositive law is $p\to q≡\neg q\to\neg p.$ Let $p=$ " $n$ is even", $q=$ " $4n^2- 3$ is odd". Then the contrapositive of the given statement is "If $4n^2- 3$ is even, then $n$ is odd".

Answer: 2. False