Question

Determine which, if any, of the three statements are equivalent.
a.) If you are fishing at 1 p.m., then you are driving a car at 1 p.m.

b.) You are not fishing at 1 p.m. or you are driving a car at 1 p.m.

c.) It is false that you are fishing at 1 p.m. and you are not driving a car at 1 p.m.

Answer 1

The conditional form (if P, then Q) and the contrapositive (if ~Q, then ~P) are logically equivalent. In this case, you have
P: You are fishing at 1 p.m.
Q: You are driving at 1 p.m.

a): If (P) then (Q)
b): If (~P) then (~Q)
c): If (~P) then (~Q)

a) isn't logically equivalent to b) or c) because they are not contrapositives (they are inverses)
b) and c) are saying they same thing, so b) and c) are logically equivalent.

Answer 2

thanks

Answer 3

No worries :)