Question

What is the truth value for the following conditional statement?

p: false
q: false

∼p → ∼q

T F → T
F T → F
F F → T
T T → T

Answer 1

TT→T

Explanation:

If p is false, then ~p is true.

If q is false, then ~q is true.

Now note that

• If a and b are both true, then a→b is true.
• If a is true, b is false, then a→b is false.
• If a is false, b is true, then a→b is true.
• If a and b are both false, then a→b is true.

In your case, both~p and ~q are true, then ~p→~q is true too (or TT→T)