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

EXERCISE 1.6Q 2.2   PAGE 16

Exercise 1.6 | Q 2.2 | Page 16

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

(~ q ∧ p) ∧ (p ∧ ~ p)

SOLUTION

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

All the truth values in the last column are F. Hence, it is a contradiction.