Prove: ( A B ) * C= ( A * B ) ( B *C ) Where: A B = { x : (x in A) xor (x in B)}

Question

Prove: ( A B ) * C= ( A * B ) ( B *C ) Where: A B = { x : (x in A) xor (x in B)} A * B = { x * y : (x in A) and (y in B)} In other words is the symmetricdifference of two sets and * is the concatenation of two sets andx*y is the concatenation of two elements in the set. Prove: ( A B ) * C= ( A * B ) ( B *C ) Where: A B = { x : (x in A) xor (x in B)} A * B = { x * y : (x in A) and (y in B)} In other words is the symmetricdifference of two sets and * is the concatenation of two sets andx*y is the concatenation of two elements in the set. Where: A B = { x : (x in A) xor (x in B)} A * B = { x * y : (x in A) and (y in B)} In other words is the symmetricdifference of two sets and * is the concatenation of two sets andx*y is the concatenation of two elements in the set.

Explanation / Answer

Dear,
Proof: A B C (A XOR B) (A XOR B) *C (A*C) (B*C) (A*C)XOR (B*C) T T T F F T T F T T F F F F F F T F T T T T F T T F F T F F F F F T T T T F T T F T F T F F F F F F T F F F F F F F F F F F F F ( A B ) * C= ( A* C ) ( B * C ) ; NOT B,i.e., C Proved in Tautology method. A B C (A XOR B) (A XOR B) *C (A*C) (B*C) (A*C)XOR (B*C) T T T F F T T F T T F F F F F F T F T T T T F T T F F T F F F F F T T T T F T T F T F T F F F F F F T F F F F F F F F F F F F F

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