Examine whether the following statement pattern is a tautology, a contradiction or a contingency. ~ p → (p → ~ q)

EXERCISE 1.6Q 2.4   PAGE 16

Exercise 1.6 | Q 2.4 | Page 16

Examine whether the following statement pattern is a tautology, a contradiction or a contingency.

~ p → (p → ~ q)

SOLUTION

p	q	~p	~q	p→~q	~p→(p→~q)
T	T	F	F	F	T
T	F	F	T	T	T
F	T	T	F	T	T
F	F	T	T	T	T

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