Prove the following using mathematical induction. a. For sets, (B1 B2 n ... n Bn)' = (B'₁ U B'2 U ... U B'n) b. For all positive integers n, 12 +2² + 3² + ... + n² = c. For all positive integers n, n(n+1)(2n+1) 6 - 1 + 3 + 5 + ... + (2n − 1) = n² d. For all positive integers n, + 1 1-2-3-4 n + + + = n(n + 1) n+1

Q: (a) Prove by mathematical induction that the following statement is true for every positive integer…

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Q: Prove by induction that the following statement is true for all positive integers. 2³n— 1 is…

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Q: n(n+1)(2n+1) Prove: 12 + 22 + 3² + ... +n? for all positive integers, n.

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Q: 1 Use Mathematical Induction to prove that 2 k2 k=1

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A: (b) Case 1 : n=1 2×1!+5×2!+10×3!+...+(12+1)1! = 1(1+1)!2×1! = 1(2)!2 = 2 Therefore, the result is…

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A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

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Q: Prove that the statement is true for every positive integer n.

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Q: 1. Prove by induction that for all n € N>1 we have (a) (b) (c) 2 +3 2.3 9+ (9 × 10) + (9 × 100) ++…

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A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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Q: Q1: For A = (-3,-2, ... , 4} and B = {1, 2, . .. , 6}, determine S = {(a, b) e A x B: a+b² = 25}.

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A: The solution is given as

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Q: 1. Prove by induction that for all positive integers n, we have: 1+3+5+ + (2n 1) n2

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Q: (1) Let A = {1, 2, 3, 4}, B = {2, 4, 6}, C = {1, 3, 5} and U = {1, 2, 3, 4, 5, 6, 7}. Compute the…

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Q: (16) Prove that 22n – 1 is divisible by 3 for all n € N.

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