a) Claim. If and thenProof. Assume and Then there exists a function fsuch that Since
Chapter 5, Problem 17(choose chapter or problem)
a) Claim. If and thenProof. Assume and Then there exists a function fsuch that Since Therefore, (b) Claim. If and thenProof. Suppose Then B is a proper subset of C. ThusThis implies But and,since B and are disjoint, By hypothesis,Thus a contradiction.(c) Claim. If and thenProof. Assume andCase 1. Then by substitution inCase 2. Then by transitivity, (d) Claim. If and then there exists a functionProof. Assume Then there exists a functionSince g is one-to-one, every b in B has exactly one pre-image in A. Thusthe set is the pre-image of b under g} is a function. Thisfunction is onto A, because for each a in A, and so
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