Let A and B be nonempty sets of real numbers. If sup B exists then sup (A U B) exists if A is bounded .a O inf B s sup B .b O the set A U B is bounded above .c O sup(B) s sup (A U B) .d O

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A: To findElement of (say)A={x| x is an integer number such that x2=2}

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Q: 1] Find the supremums of the following sets by proving your results: a) S = {a < x < b; x E R}. b)…

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A: Let A=1, 2, 3, B=a, b, c

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A: Sup(A) denote  least upper bound of set A

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Q: If S is a non-empty set of real numbers which is bounded above, then a real number s is the supremum…

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Q: Let A and B be nonempty sets of real numbers. If sup A exists then: a. sup (A U B) exists if sup(B)…

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Q: (b) Let A = (x ER 0<x< 1) and B=(x ER | 0<x<2). Determine whether A and B have the same cardinality.

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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A: SOLUTION-

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Q: (b) Let A = a + 1 and B = b+ 12. Using proof by induction, show that A+B divides An+1 + Bên+1, What…

A: here i used basic condition of divisibility and i used the notation a|b for a divides b .

Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B)n (A × C)

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Q: (b) Let A = (x ER 0<x< 1} and B = {x ER|0<x<2}. Determine whether A and B have the same cardinality.

A: Solution:-

Q: The set A={x: xEN,x^2-3x+2 = 0} is %3D Null set Finite set Infinite set None of these

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Q: Let A be a nonempty subset of positive integers and B = {n + v5_ : nE A}. Show that B has a least…

A: We will use the well ordering principle to prove that B has a least element.

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Q: 2 Let A and B be two measurable setsa prove that ie BAIS measurable and mCB\A) =M CB)-mcA) %3D

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