5. Suppose that A = = {0,1} and B = {0}. (a) Write down the elements of AU B. (b) Write down the elements of P(AUB). Write down the elements of A× P(B). (d) Find a set S that is, like the sets in parts (a)- above, built up out of A and B through some combination of taking power sets, unions, intersections, and Cartesian products (but you are not required to use all these operations). Your set S must have the following two features:- S has exactly 10 elements;- (1,0) is an element of S.

Q: You have 10 of each of the following type of objects: A, B, C, and D. The objects of each type are…

A: 1. There are total 40 different objects, 10 belonging to each of types A, B, C, and D- A1, A2, …,…

Q: In this question and subsequently, let d₁, d2, ..., d5 denote the first five digits of your exam…

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Q: this question and subsequently, let a₁, A2,..., a5 denote these numbers: 2,2,1,7,3 Let X denote the…

A:

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: For two sets A and B, if A=B, then (i) A and B have the same elements (ii) ACB and BCA (iii) x €…

A: Here we have to find the properties of two sets A and B is A= B.

Q: Use an element argument to prove the following statement.. Proof: For all sets A, B, and C, An (B-C)…

A:

Q: In the Axiom Systems section of the Background chapter (1.6), a binary relation <on a nonempty set X…

A: Given X is a set consisting of 64 teams.  Let ⩽ be the relation on X such that for a,b∈X, a≤b…

Q: Please answer a, c & h

A: The given sets are as follows. U=N=1,1,3,4,…A=x∈N| x≥7=7,8,9,…B=x∈N|x is odd=1,3,5,7,9,…C=x∈N|x is a…

Q: 4. Is the set Q² x {a,b,c} countable or uncountable? You must justify your answer with a proof.

A: Given : ℚ2×a , b ,c  To Prove : ℚ2×a , b ,c  countable or uncountable

Q: Determine if the following sets are closed under multiplication. a. (1,18) b. {2k + 9|keW} c.…

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Q: Theorem 5.25. Let A, B, and C be sets. Then 1. A× (B N C) = (A × B) N (A × C) 2. A × (B U C) = (A ×…

A:

Q: (a) Let A, B be sets. Prove that A\(An B) = A\B. You may assume all sets in the question are…

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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: Let A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Give an example of three sets, A1, A2, and A3, such that…

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Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

A:

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

A:

Q: Let A = {7m +1 : m € Z} and B = {14n – 6 : n € Z} be subsets of a universal set U. Justify why A ¢ B…

A: Consider the given sets:

Q: Let A and B be any sets. Show that: (a) A – B, B - A, and An B are disjoint with each other. (b) A =…

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Q: 5. For finite sets A and B, which of the following equals |A x B], the cardinality of the Cartesian…

A: Cartesian product :  Let two sets  A and Bthen the Cartesian product  A×B is  given by ,  A×B =  (…