The following is the converse of a conditional statement. if it is not april 17th, then it is not matt's birthday. what is the inverse of the original conditional statement?

1. Let p and q be the following statements:

p: It is not April 17th
q: It is not Matt's birthday.

p⇒q is the conditional statement "If it is not April 17th, then it is not Matt's birthday."

the inverse of the conditional statement p⇒q is ¬p⇒¬q so we need to negate both p and q:

¬p: not p ≡ not (It is not April 17th) ≡ It is April 17th
¬q: not q ≡ not (It is not Matt's birthday) ≡ It is Matt's birthday

¬p⇒¬q: If (not p) then (not q) ≡ if (It is April 17th) then (It is Matt's birthday)
≡ "if It is April 17th then It is Matt's birthday"