Question

Which of the following are equivalent statements to the implication $p\to q$.

• A.
• B.
• C.
• D.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

B

C

D

Let's analyze the question by looking at the truth table of the implication.

From the truth table its clear that $p\to q$ is equivalent to $\sim q\to \sim p$.

Let's consider option (d). s1: "q is a necessary condition for p” which means for an implication of truth value T, q has to be necessarily 'T' for the value of p to be 'T'. And if it's not so implication assumes value 'F'.

In option (c) s2: "p is a sufficient condition for q”. We can check this by seeing that for implications a truth value of T for p is ensuring a truth value T for q also. If its ensured truth value of implication is T or else F.

Option (b) is only a rephrased version of option (d).