Question

What is the difference between the converse of a statement and the contrapositive of a statement? Do
they have the same truth value?

Answer 1

If p then q

the converse of this is q->p

the truth value is this

p q p-> q q -> p
T T T T
T F F T
F T T F
F F T T

i'll let you decide what that means

Answer 2

the conditional \[A\Rightarrow B\]
the converse of the conditional is
\[B\Rightarrow A\]
the contrapositive of the conditional is
\[\neg B\Rightarrow \neg A\]

Answer 3

for contrapositive, it's \(\neg\)q -> \(\neg\)p

the truth value is

p q p-> q q -> p ~q->~p
T T T T T
T F F T F
F T T F T
F F T T T

Answer 4

converse is positive contrapositive is negative