In: Computer Science
Prove the following set identity using logical equivalences: A ∪ (B - A) = A ∪ B.\
(Hint: Insert a table with 2 columns and 8 rows.)
A (B - A) = A B
L.H.S. = A (B - A)
= A (B ∩ AC) {Set Difference Law, A - B = A ∩ BC }
= (A B) ∩ (A AC) {Distributive Law, A (B ∩ C) = (A B) ∩ (A C)}
= (A B) ∩ T {Complement Law, A AC = T }
= (A B) {Identity Law, A ∩ T = A }
= R.H.S.
As, L.H.S. = R.H.S.. It is clear that A (B - A) = A B is logically equivalent.
If you're still having any doubt then please feel free to ask in the comment section.