Prove the following statements. a. Let a € Z, then 3|(2a² + 1) if and only if 3 a. b. Let a € Z. If 2|(a² – 5) then 4|(a²-5). (Hint: For justification you might want to use Q5b). c. Let a € Z. If 2(a² − 1) then 8|(a² − 1). d. If a is an integer and a²la then a € {−1,0, 1}. e. Let a, b, c € Z if a² + b² = c² then 3|ab.

Q: Then A-1 If A = 5 1 -16 -3 0 0 0 -1 0 w 00+ 4 -13

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Q: Suppose a,b,c€Z. If a |b and a |c, then a|(b+c).

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Q: Reject Ho if |z| > N

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A: Given  W​ = {0,1,2,3,...}, L={x | x =2n+1, n ∈ W}​, M={x | x =2n, n ∈ W}​, and N​ = {1,2,3,...}

Q: 7. Find U₁A; and №ºA; if i € N and A; = {x|x € Z, −i ≤ x ≤ i}. Write a 1 sentence justification for…

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Q: 18. Show that P→ qand-q→→p are logically equivalent.

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Q: 1. Determine the following, if g = [3, -2,5] and h = [4, 1, −6]. a) g + h b) g- h c) g.h d) Igl

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