Consider two sets, A = {1, 2, 3, ..., 100} and B = {3, 5, 7, 9, ... , 201}. Prove that |A| = |B| by first finding a bijection f : A→B, and proving that f both an injection and a surjection.

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Q: Assume that A and B are nonempty, bounded above, and satisfy B CACR. Show that sup B < sup A.

A: Introduction: The supremum and infimum properties are the very important properties of any subset of…

Q: 2. 1. 5. 2. up 2. Example, :find the produck ר

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A: The answer is given as follows:

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A: To prove  the given function surjective we will use the fact that each f(i) is surjective

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Q: Q.No.3 a) Prove that if A and B are sets, then (An B)U (ANB') = A

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A: Inverse image of closed set is closed. Whenever f is continous from that we solved this question.

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Q: I need help for number 7. Thanks!

A: (a)Let

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A: First we have to divide the set into finite subsets of x intervals required.