Question: 1. Simplify the following set expressions. (1) ((AB)B)(AB) (2) ((ABC)(BC))A 2. Let A and B be sets, prove: (AB)(BA)=(AB)(AB) 3. Prove the following set identities.

1. Simplify the following set expressions. (1) ((AB)B)(AB) (2) ((ABC)(BC))A 2.

1. Simplify the following set expressions. (1) ((AB)B)(AB) (2) ((ABC)(BC))A 2. Let A and B be sets, prove: (AB)(BA)=(AB)(AB) 3. Prove the following set identities. (1) A(BA)=BA 4. Find the necessary and sufficient conditions for the following set equations to be satisfied. (1) (AB)(AC)= (2) (AB)(AC)=A

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