Classify each of the following subsets of R as compact, connected, neither, or both. Justify your answer. (a) {1, 2, ... , 100} (b) [0, ∞) Please include interval notation (with a line) for (a) and (b). Thanks!

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Q: 2. For each of the following relations on the set {1,3,4, 7}. • R1 = {(7, 7), (1, 1), (4, 4), (3,…

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Q: (a) Explain with cases why, if a is a real number,  then a ≤ |a|. (b) Explain, if, for any real…

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Q: Draw the relation

A: Given: x,y/x2+y2≤1 To draw: The relation.

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Q: d) Let the set A = {1, 2, 3,4} and let P(A) denote the power-set of A. Consider the following…

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Q: [2.28] Which of the following sets are convex and which are not? a. {(x₁, x₂) x² + x² ≥ 3}. : b.…

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Q: (a) Prove that the function f is well-defined; that is, the value f(q) of the function at a rational…

A: Given the notation , and using this defining the set . Then the function  defined as:.It is well…

Q: 4. Describe the image of the following sets under the following maps (a) f(2)= for S S = {0}; (b)…

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Q: What is the domain of g(x,y) =; ху Select the correct choice below and fill in any answer boxes…

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Q: T or F True or not: Every nonempty set of rational numbers that is bounded has a largest number.

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Q: 7. Compute gfg, the conjugate pair of f by g for f= (2, 3, 5, 4) and g = (1, 3, 2)(4, 5).

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Q: Proof the following statement in detail: ". Let x ∈ R. Prove that if 3x4 + 1 ≤ x7 + x3, then x >…

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Q: Q: State whether the following statements are true or false: 1. Let S be a non-empty subset of the…

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Q: Consider the relation R = {(1,1);(2,3);(3,5);(4,7)}. a. Prove that R is a function from {1,2,3,4}…

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