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

EXERCISE 1.6Q 4.4   PAGE 16

Exercise 1.6 | Q 4.4 | Page 16

Prove that the following statement pattern is a contradiction.

(p → q) ∧ (p ∧ ~ q)

SOLUTION

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

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