Using the truth table, prove the following logical equivalence. p ∧ (~p ∨ q) ≡ p ∧ q

QUESTION

Miscellaneous Exercise 1 | Q 4.14 | Page 33

Using the truth table, prove the following logical equivalence.

p ∧ (~p ∨ q) ≡ p ∧ q

SOLUTION

1	2	3	4	5	6
p	q	~p	~p∨q	p∧(~p∨q)	p∧q
T	T	F	T	T	T
T	F	F	F	F	F
F	T	T	T	F	F
F	F	T	T	F	F

In the above truth table, the entries in columns 5 and 6 are identical.

∴ p ∧ (~p ∨ q) ≡ p ∧ q