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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

pq~p~qp∧q~p∨~q(p∧q)∧(~p∨~q)
TTFFTFF
TFFTFTF
FTTFFTF
FFTTFTF

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