The number of non-empty subsets of Bis 2 |{S:SC A, |S| = 2 and Sn B=0}|= 2 max {|S| : S C AUB, |SN A| is even and |Sn B| is even} = 4

Q: Which of the following sets are well-ordered. Justify youranswer carefully.A.{x:xEZ, X…

A: A set of numbers is well ordered when each of its nonempty subsets has a minimum element.

Q: 1. example of sets A and B for which A B but Ag B.

A: Cardinality of a set is number of elements in the set.

Q: Prove that the set {a E R: a2 not equal to 6} is open.

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Q: , B, and C which satis

A: Given as, A= {1, |B|, |C|} B= {2,| A|, |C|} C= {1, 2, |A|, |B|}

Q: Assume that a and b are real numbers such that a <b. Prove that the interval (a,b) is an open set.…

A: Given that a and b are real numbers and a&lt;b. Prove that (a,b) is an open set

Q: For set A={9,10,11,12,13,14} and set B, the set of all natural numbers between 8 and 14 inclusive,…

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Q: 1. Let A = [1, 3], B = (2, 5], and C= {2}. Write the inequalities (or equalities) that specify each…

A: We will just use of definitions of different type of sets

Q: 4) Let a < b be real numbers. Prove that the half open/half closed interval (a, b) is both an Fo and…

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Q: Let A= {k: k ∈ N, k ≤ 20}, B= {3k−1: k ∈ N}, and C= {2k+1: k ∈ N} 1. A INTERSECTION B INTERSECTION…

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Q: Let A and B be arbitrary sets. For each statement below, decide whether it is true or false. If the…

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Q: Suppose A and B are finite sets with |A| = a, |B| = b and |An B| = c. Find (a) |AB| (b) AX (AUB)|…

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Q: Identify which sets are equal A = {0,1,2} B = {x ∈ R | -1 ≤ x < 3} C = {x ∈ R | -1 < x < 3} D =…

A: We identify which sets are equal.

Q: Given the sets C = {1, -3} and D = {2, 3, 6}, find all ordered pairs (x,y)and those that satisfy the…

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Q: The sets A, B, C and D are defined as follows: A = {-1, 0, 1, 2, 3} B = {1/2, 1, 4} C = {x | 0 &lt;…

A: The sets A, B, C and D are defined as follows: A = {-1, 0, 1, 2, 3} B = {1/2, 1, 4} C = {x | 0 &lt;…

Q: Let A and B be finite sets such that B = {b1, b2}. Prove that |A – B| < |A|.

A: We are given that A and B are two finite sets, where B= {b1, b2}.We have, |B| = 2, and let |A| =…

Q: Let A, B, C be sets. Prove that if C ⊆A, then A −(B −C) = (A −B) ∪C. Analogously, for any real…

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Q: Let A and B be nonempty sets. Prove that A x B = B x A if and only if A = B.

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Q: Challenge. Establish the Cauchy-Schwartz inequality: For real numbers we have (a + az + ..+ a) (b+…

A: Prove the Cauchy-Schwartz inequality…

Q: Let A, B, and C be sets. Prove that: Ax (B\C) = (A × B) \ (A × C).

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Q: (a) For all sets A, B, C, A × (BU C) = (A × B) U (A × C). (b) For all sets A and B, P(AUB) ≤ P(A)…

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Q: Provide examples of sets A and B where strict inequality sup(A+B) < sup A+ sup B holds.

A: We have to given an example to prove given inequality:

Q: Suppose A and B are two finite sets such that |B| = 2 |A| and the number of relations on A is 16.…

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Q: Which of the following sets are convex and which are not? 2 a. {(x₁, x₂) x² + x²₂² ≥ 3}. b. {(x₁,…

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Q: Show that for every pair of sets X and Y, the sets X × Y and U {(x, y) | y ≤ Y} xEX are equal.

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Q: C = lq² + 1 | p, q € Z,0 < p < 1 and – 1< qs -1s95}

A: We will solve the problem

Q: Let A E R2x3, be R². Determine whether or not S = {x R³ | Ax=b, x₁ ≤ 0, x₂ ≤ 0} X2 sa convex set.

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Q: Show that the interval [0,1] is a closed set in R

A: