Question

What is the logical equivalent of the converse of the contrapositive of a conditional statement?

conditional
contrapositive
converse
inverse

Answer 1

conditional

converse means opposite
contrapositive also means opposite
hence the opposite of the opposite would be the original

that sentence was a double negative in a sense^^

Answer 2

Wrong.

Answer 3

The contrapositive has the same truth value as the original.

Answer 4

Original \(P\to Q\)
Converse \(Q\to P\)
Contrapositive \(\lnot Q\to \lnot P\)
Inverse \(\lnot P\to \lnot Q\)

Answer 5

oh right so a contrapositive is simply another way of stating the original sentence

Answer 6

First we go to the contrapositve: \(\lnot Q\to \lnot P\)
If we said \(P'=\lnot Q\) and \(Q' = \lnot P\), then we have \(P'\to Q'\)
The converse of this would be \(Q'\to P'\).
Undoing the substitution beings us back to \(\lnot P\to \lnot Q\).
Notice that this is identical to the Inverse of the original.