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

EXERCISE 1.6Q 2.3   PAGE 16

Exercise 1.6 | Q 2.3 | Page 16

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

(p ∧ ~ q) → (~ p ∧ ~ q)

SOLUTION

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

The truth values in the last column are not identical. Hence, it is contingency.