Prove that the following statement pattern is a tautology. (p → q) ↔ (~ q → ~ p)

EXERCISE 1.6Q 3.2   PAGE 16
Exercise 1.6 | Q 3.2 | Page 16

Prove that the following statement pattern is a tautology.

(p → q) ↔ (~ q → ~ p)


SOLUTION

pq~p~qp→q~q→~p(p→q)↔(~q→~p)
TTFFTTT
TFFTFFT
FTTFTTT
FFTTTTT

All the truth values in the last column are T. Hence, it is a tautology.