State if the following is closed under addition. If it is closed, prove and explain why. If it is not closed provide a counterexample. {3, 6, 9, 12, ...}

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Q: Prove the following statement: 2" ≥ 2n

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Q: Find a pair of integers x and y such that 66x + 48y = gcd(66, 48)

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Q: 4] Let x, YER Using proof by contradiction, prove that VxVy(512y3+8x2y<x³+64y2x⇒8y<x)

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Q: If Ua = {(x1, x2, x3)" E R³|x1+ 2x2 + 3ax3 = a} is closed under addition, then a = 0. Prove that the…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: What property of congruence is illustrated in the following? If ∠X ≅ ∠Y and ∠Y ≅ ∠Z , then ∠X ≅ ∠Z .…

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Q: Which of the following sets are closed under addition? Choose ALL that apply.

A: A set A is closed under addition, if for every x and y belong to A then x+y also belong to A.

Q: The supremum of the set S={1- (-1)". :neN is a) 1 b) 0 c) п d) 2

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Q: Which of the following sets are closed under multiplication?

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Q: Let (a,b)=1 Show that (a+b, a-b)=1 or 2. When is this GCD 1? When is 2?

A: Proof:It is given that gcd(a,b) = 1. So ax + by = 1.Let gcd(a + b, a – b) = d, then d|( a + b) and…