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

`\\eg p \rightarrow \\eg q`

The contrapositive is

'If not q then not p'

written symbolically as

`\\eg q \rightarrow \\eg 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.