Q.43 The contrapositive of “If x and y are integers such that x y is odd, then both x and y are odd” is
A. If both x and y are odd integers, then x y is odd.
B. If both x and y are even integers, then x y is even.
C. If x or y is an odd integer, then x y is odd.
D. If both x and y are not odd integers, then the product x y is not odd.
Answer: D. If both x and y are not odd integers, then the product x y is not odd.
Explanation:
Let \mathrm{p}: x and y are integers such that x y is odd.
q : both x and y are odd.
\therefore \quad Given statement is \mathrm{p} \rightarrow \mathrm{q}
\therefore \quad Its contrapositive is \sim \mathrm{q} \rightarrow \sim \mathrm{p}
\therefore \quad Option (D) is correct.