Prove that the following statement pattern is a contradiction. (p ∧ q) ∧ (~p ∨ ~q)

EXERCISE 1.6Q 4.3   PAGE 16

Exercise 1.6 | Q 4.3 | Page 16

Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ (~p ∨ ~q)

SOLUTION

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

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