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Simplify proof
Substitute (A ^ B)
(((A & B) ^ (A | B)) & (A ^ B)) = (((A & B) ^ (A | B)) & ((A & B) ^ (A | B)))
((A & B) ^ (A | B)) & ((A & B) ^ (A | B)) = (A & B) ^ (A | B)
And (A & B) ^ (A | B) = A ^ B --- first equation
Therefore
(((A & B) ^ (A | B)) & (A ^ B)) = A ^ B
AND xor OR
You are viewing a single comment's thread. Return to all comments →
Simplify proof
Substitute (A ^ B)
(((A & B) ^ (A | B)) & (A ^ B)) = (((A & B) ^ (A | B)) & ((A & B) ^ (A | B)))
((A & B) ^ (A | B)) & ((A & B) ^ (A | B)) = (A & B) ^ (A | B)
And (A & B) ^ (A | B) = A ^ B --- first equation
Therefore
(((A & B) ^ (A | B)) & (A ^ B)) = A ^ B