question archive For each of the following claims, determine whether the claim is true or false and give an apprOpriate justi?cation

For each of the following claims, determine whether the claim is true or false and give an apprOpriate justi?cation

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For each of the following claims, determine whether the claim is true or false and give an apprOpriate justi?cation. Hint: First try to write a proof that proves the claim is true. If you succeed, then the proof is true, and the proof you wrote counts as justi?cation that the claim is true. If you get stuck, then you should consider the possibility that the claim is false. Try to come up with a counterexample (i.e., speci?c sets A, B,. . .) that proves the claim is false. If you ?nd a counterexample, then you know the claim is false, and your counterexample counts as justi?cation that the claim is false. (a) For all sets A, B, C, and D, if A Q B, then A F] C Q (C U D) H B.(3 points) (b) For all sets A and B: A U B Q A.(9 points) (c) For all sets A, B, C, and D: A H B Q (A U 0) 0 (A U D).(3 points) (d) For all sets A, B, C, and D, if B U C Q D, then A n B Q (A U C) H D.(9 points) (e) For all sets A, B, and C: if A Q C, then A U B Q B H C.(9 points) (f) For all sets A, B, C, D, and E: if AU B Q C, then D\C Q D \ (ADE).(9 points)

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