Question

By using truth table, verify if the following proposition is valid or not.

(~X ⇒ Y) ∧ X = (X ∧ ~Y) ∨ (X ∧ Y)

Answer 1

To verify the expression we need to create the truth table:

X	Y	~X	~X ⇒ Y	(X ∨ Y) ∧ X	(X ∧ ~Y) ∨ (X ∧ Y)
0	0	1	0	0	0
0	1	1	1	0	0
1	0	0	0	0	0
1	1	0	1	1	1

Since both expressions provide the same result, the proposition is valid.