Question

Which set of statements always have the same truth value?

Answer 1

Let p and q be two propositional statements,

The conditional of the two statements is

'If p then q'

written symbolically as

$p \rightarrow q$

The converse is

'If q then p'

written symbolically as

$q \rightarrow p$

The Inverse is

'If not p then not q'

written symbolically as

$\neg p \rightarrow \neg q$

The contrapositive is

'If not q then not p'

written symbolically as

$\neg q \rightarrow \neg p$

In order to determine which pairs have the same truth value, we draw a truth table as in the diagram.

We can see from the diagram that the conditional and the contrapositive have the same truth value.

The correct option is D.