If S and T are two sets such that S has 21 elements, T has 32 elements, and   S ∩ T has 11 elements, how many elements does S ∪ T have?

Q: Suppose that A, B, and C are sets. Prove that if AC B, then AnC C BN C. Disprove that if An C CBn C,…

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Q: Let A = {Janet, Jello, Justin}, B = {Sally, Solly, Molly, Jolly, Jello}, and C = {June, Janet, Jill,…

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Q: Suppose that A = all current students at MPC and B = all current students at Hartnell (and U = all…

A: Given, A = all current students at MPC and B = all current students at Hartnell

Q: Given the sets A = {0, 1, 3}, B = {1, 4, 5}, and C = {0, 1, 3, 4, 5}, what is A ∩ B ∩ C?

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Q: If A, B,C, and D are sets, does it follow that (A ⊕ B) ⊕ (C ⊕ D) = (A ⊕ C) ⊕ (B ⊕ D)?

A: The symmetric difference between the set is associative and commutative. So, (A⊕B) ⊕C=A⊕(B⊕C)…

Q: When A, B, and C are sets, A∩(B⋃C) = (A∩B)⋃C if and only if     A ∩ C ⊆ A ∩ B     C ⊆ A     A…

A: According to the given information it is required to tell that when the below statement holds.

Q: Consider the following two sets:   A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} B = {–9, –6, –3, 0,…

A: The intersection of two sets A and B contains the elements that the two sets have in common.

Q: If U is the set of all multiples of 3 less than 20, and M={3,12,18}, find Mc (the complement of M).…

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Q: If A and B are both finite sets and A has n elements and B has m elements, what’s the fewest number…

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Q: Suppose that A and B are two sets. (a) If n(A ∪ B) = 22, n(A ∩ B) = 8, and n(B) = 12, find n(A). (b)…

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Q: How many distinct four-letter "words" can you form using all the letters of SETS?

A: We have to find no of distinct four letter can be formed using all letter of word SETS.

Q: Let A, B, C, and D be sets.

A: First, (AxC)U(BXD) ⸦(AUC) x(BUD)Take left hand side first , let  (x,y) ∈(AxC) U(BxD)=> (x,y)…

Q: Find the number of elements in A1 ∪ A2 ∪ A3 if there are 135 elements in each set and if the sets…

A: We have to find the number of elements in A1 ∪ A2 ∪ A3 if there are 135 elements in each set and if…

Q: Give an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

A: We construct  an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

Q: Let A = {July, John, James, Jared, Jeniffer, Jelly}, B = {John, Jelly, Jared}, and C = {Irina,…

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Q: If A and B are any two sets and AUB = . A n B, then

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Q: Find the sets A and B if A − B = {1, 4, 7, 11}, B − A ={2, 20}, and A ∩ B = {3, 5 ,19}

A: Set Question

Q: Let A be a set with 5 elements and B be a set with 8 elements.  How many elements are in A x B?

A: Given that A be a set with 5 elements and B be a set with 8 elements.  Here we have to find out how…

Q: Let A = {July, John, Jill, Jared, Jeniffer, Jelly), B = (John, Jelly, Jared), and C = {Irina, Irena,…

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Q: Let A = {June, John, James, Justin, Jeffrey, Jelly}, B = {John, Jelly, Justin}, and C = {Irina,…

A: Let A = {June, John, James, Justin, Jeffrey, Jelly}  B = {John, Jelly, Justin} C = {Irina, Irena,…

Q: Let A = {Becca, Darius, Julian, Larry, Solly, Bess), B = {Larry, Solly, Darius}, and C= {Mellie,…

A: Given that                      A={Becca, Darius, Julian, Larry, Solly, Bess}…

Q: Find the sets A and B if A − B = {1, 5, 7, 8}, B − A = {2, 10}, and A ∩ B = {3, 6, 9}.

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Q: If the set A has 3 elements and the set B = {3, 4, 5}, then find the number ofelements in (A×B).

A: Given that n(A)=3 From B = {3, 4, 5} we see that n(B)=3

Q: If A,B and C are sets, then (AUB)-C=(A-C)U(B–C).

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.