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.
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