Determine whether the following statement pattern is a tautology, contradiction, or contingency. [~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]

QUESTION

Miscellaneous Exercise 1 | Q 4.13 | Page 33

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

[~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]

SOLUTION

p	q	~p	~q	p∨q	~(p∨q)	~(p∨q)→p	(~p)∧(~q)	[~(p∨q)→p]↔[(~p)∧(~q)]
T	T	F	F	T	F	T	F	F
T	F	F	T	T	F	T	F	F
F	T	T	F	T	F	T	F	F
F	F	T	T	F	T	F	T	F

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