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1) Use a membership table to determine whether or not the following is true. Do not simplify the sides first. A - (Bn C) - (A-B) U(A - C) 2) Prove the following by using laws of logic (i.e. using an assertion/reason: format proof, as seen on page 104 of the Course Notes): - 3) For each positive integer k, let Ak - {x € z| - <2k}. List out the elements that are members of the following 3 (a) Ak k-1 3 (b) U k-1 4) (a) By demonstrating a counter-example, show that the function, f(x) - x² + 4, where f E - z, is not injective (not one-to-one). (b) Prove, f(x) - 5x + 2, where f E - RE, is surjective (onto).

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Set Operations and Properties of Functions
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