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: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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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: State whether the following claim is true and explain why. (a) Claim: For all sets A, B, and C: (A –…

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Q: Suppose that |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2. Determine the smallest that |A…

A: Given, |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2

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: 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: Prove if the following statement is true or disprove if it is false. If A and B are finite sets,…

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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: 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: For the four pairs of sets below, determine whether or not they are equipollent. i.) {2, 5, 10} and…

A: We have to find the equipollnt sets from the given pair of four sets.

Q: If the light is off 17 plack socks and 17 white socks if the light is off and Matt reaches into the…

A: If he pulls 2 socks, then he might get one black sock and one white sock. So, n≠2

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: 3. Given X = {x|x-2}, and Z = {x|x< -3}, write the union or intersection in set-builder notation. а.…

A: Given that, X=x| x&lt;7, Y=x| x≥-2 and Z=x| x&lt;-3 Since,  Set X represents all real numbers less…

Q: If |A|  8 and |B|  5, what is |A ∪ B| + |A ∩ B| ?

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Q: Given X = {x | x &lt; 7}, Y = {x | x ≥ −2}, and Z = {x | x &lt; −3}, write the union or intersection…

A: Let x belongs to the set of integers. Let the Given set X, Y and Z defined as:

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

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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: 5. Let the universal set be R, the set of all real numbers, and let A = {x € R| – 4 <x< 1},B = {x €…

A: Given the universal set as ℝ, the set of all real numbers. Let A={x∈ℝ| -4≤x&lt;1}, B={x∈ℝ|…

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: Which of the following sets, given by the roster method, is equal to the set below given in…

A: The objective of the question is to find the set that matches the set-builder notation {x belongs to…

Q: 1. Give the domain of y=xin set builder notation. 2. If a and b are real numbers such that a <b,…

A: Given that 1. y=1x2-42.  x-ab-x≤0

Q: each part below, indicate (by making suitable arguments) whether the following sets are open…

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Q: Let A,B be sets. Prove that AAB = if and only if A= B

A: