3. In the proofs below, you may use any of the following facts (without proving them...

   

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3. In the proofs below, you may use any of the following facts (without proving them yourself): x AUB is equivalent to (x A) V (x B) xE ANB is equivalent to (x x is equivalent to (x = A) A) A (x B) x A B is equivalent to (x = A) A(x = B) Any of the laws of propositional logic in Table 1.5.1 of the zyBook Let A, B, and C be sets. (a) (3 points) Prove that if AC B and A C C, then AC (BNC). (b) (3 points) Prove that AU (BNC) = (AUB)n (AUC). (Hint: To show that two sets are equal to each other, show that each is a subset of the other.) 3. In the proofs below, you may use any of the following facts (without proving them yourself): x AUB is equivalent to (x A) V (x B) xE ANB is equivalent to (x x is equivalent to (x = A) A) A (x B) x A B is equivalent to (x = A) A(x = B) Any of the laws of propositional logic in Table 1.5.1 of the zyBook Let A, B, and C be sets. (a) (3 points) Prove that if AC B and A C C, then AC (BNC). (b) (3 points) Prove that AU (BNC) = (AUB)n (AUC). (Hint: To show that two sets are equal to each other, show that each is a subset of the other.)

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a Given that A B and A C we need to prove that A B C To prove this we need to show that every elem... View the full answer