Let n E N. Prove that if |n − 1| + |n + 1| ≤ 1, then |n² − 1| ≤ 4.

Q: (b) For all integers n, if n² is odd, then n is also odd.

A: Given statement: For all integers, if n2 is odd, then n is also odd. Prove this statement by…

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Q: not use ai please

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Q: Prove Vn € N, 1 1 + 1 2 + 1 3 + + 11 2n - 1 + 2n ≥1+ n 2

A: Let's prove the given inequality step by step:Base Case (n=1):11≥1+12This is true, as 11=1 and…

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Q: what are the integers for 6<x<7 with a line under each less than sign

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Q: 3. Prove that any Integens . Proof (by contradicton): ,9 t (a?-3)

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Q: Prove for all integers n, k, and r with n ≥k≥r that (O)(=O(-) Lify both sides.) n n- r

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Q: i Express the set: = {n € N|(-11 < n) ^ (n mod 7= 4) ^ (n < 10)} by explicitly writing each item in…

A: i. Consider the set S=n∈ℕ|-11≤n∧n  mod 7 = 4∧n&lt;10. From the inequalities -11≤n and n&lt;10, we…

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Q: what are the integers of 4 < x < 6

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Q: Using strong PMI, show that every natural number is a sum of powers of 2. For example, 11 = 23 +2¹…

A: Using strong PMI, we have to show show that every natural number is a sum of powers of 2.