Let A = {1, 2, 3}, B = {u}, and C = {m, n}. Find each of the following sets.a. A X (B X C)b. (A X B) X Cc. A X B X C

Q: Let A %3D {a, b, с}, В %3D {b, с, d}, and C %3D {ь, с, е}. (a) Find A U (B n C), (A U B) n C, and (A…

A:

Q: Let 4, B, and C be sets. Show that а) (А — В) — С СA-C. b) (A — C) n (С- В) — 0.

A: It can be solved by the set theory

Q: Let A. B. and C be non-empty sets. Then AXBXC=C×B×A if and only if* O B=C None of these A-C A-B3DC O…

A: See solution below

Q: b) BCA iff A n B = ¢ c) (A – B) U B = A iff B C A

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Q: For any sets A and B , (ANB) = %3D O a. ANB O b. ANB Oc. B-A С. В- А O d. U-B

A: By using identities of set theory :

Q: Let 4, B, and C be sets. Show that a) (A - B) – CSA C. b) (A - C) n (C- B) = 0.

A: Answer

Q: If R is the universal set, find: 1. Q ∩ R 2. Z ∩ I 3. N ∩ I

A: Since R is universal set.

Q: Let R = {a}, S = {x, y}, and T = {p, q, r}. Find each of the following sets.a. R X (S X T)b. (R X S)…

A: Cartesian product of set A and B is defined as:

Q: Write each of the following sets in the form of listing its elements (i.e. in the form {a,b,c} to…

A: 1). A set ∅ is known as an Empty Set (i.e., a set having no elements). Here P({∅}) is the power set…

Q: If A = {x: x |B| D. None of these {x: x 2 + 11x + 30 = 0,x E N}, then C is a/an? A. Empty set B.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Prove : a. For any sets A and B, AXB=BXA b.For any sets A, B, C (A x B) x C Ax B x C AX (BXC) c. If…

A: let the set A and B are A= ( m,n)   , B = (n,m) Now, A×B = {(m,n), (n,n),(n,m),(m,m)} B×A=…

Q: Let A, B, and C are three sets, prove that Cx (A – B) = (C x A) – (C × B) C.

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Q: Suppose A and B are sets such that |A| = 2 and |B| = 3. What is |P(A x B)|?

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Q: For every two sets A and B, if A–B = B – A , then A-B=Ø. For every two sets A and B, ANBCA-B.

A: (4) Given A and B are two set such that A-B=B-A for every A and B We have to show that A-B=∅ Now,…

Q: A [(0,6) U (7, 12)]n (2,9; B= A\({1,2, 4} U (3, 5)) and C = BU{11, 8}. Give an explicit and fully…

A: This is a problem of point-set topology.

Q: Let A = {a, b}, B = {1, 2}, and C = {2, 3}. Use set-roster notation to write each of the following…

A: (a) Find B∪C. B∪C=1,2,3 Now find A×B∪C. A×B∪C=a,1,a,2,a,3,b,3,b,1,b,2   (b) Find A×B.…

Q: Write each of the following set in form {x :x € S and P(x)} (or builder notation) a. A= {1,3, 9, 27,…

A: Here A = { 1,3,9,27....} and D = {1, 1/2, 1/4,1/8, 1/16,...} To write this in set builder notation

Q: If A,B and C are sets, then A x (B-C) = (A × B)- (A x C). |

A:

Q: If A and B are sets; A and B denote the complements of the sets A and B, then set (A- B)U(B –…

A: Using venn diagram we solve this question.

Q: Let A and B be two sets. We denote A- B = { x | x∊A and xÏB}. Prove that A∪B=(A−B)∪(A∩B)∪(B−A).

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Q: if A and B are sets, then A x B=B x A

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Q: Let A and B be sets.                                   If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for…

A:

Q: Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False.

A: Use the basic properties of intersection and cartesian product to prove the given relation.

Q: Let A and B be sets. Then B (B – A) is equal to the above A N B

A: The Venn diagram for 2 sets can be drawn as follows.

Q: Let A = {1,4,9} and B = {1,3,6,10}. Find each of the following sets. (a) A U B. (b) An B. (c) A \ B.…

A: Sets can be defined as a collection of elements . The elements that form the set can be any elements…

Q: Find sets A, B and C such that A ∩ B,    B ∩ C and A ∩ C are non-emptysets and A ∩ B ∩ C = φ.

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Q: If A, B, C are sets, show that a) A x B= 0 ⇒ A=0 or B = 0. b) (AUB) x C = (AXC) U (BxX C). c) (An B)…

A:

Q: Three sets are defined as follows: A = {x: 0 ≤ x ≤ 4} B = {x: 0 ≤ x ≤ 3} C = {x: −1 ≤ x ≤ 2} Draw…

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Q: If A and B are any two sets and A U B = A ∩ B, then a. A= Ø b. B= Ø c. A=B d. None of these

A: topic - sets option C.   A=B

Q: Let A, B, and C be arbitrary sets. Determine if the given relationship is correct or incorrect. АВС…

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Q: Show that if A and B are sets, then P(A) u P(B) C P(A u B), where P(A) denotes the power set of A

A: For a set A, the set of all its subsets is called the power set of A. Now, consider two sets A and…

Q: For all sets A and B, ifA-B=0, then A = B.

A: For all sets A and B, if A-B=∅, then A=B.

Q: Show that if A and B are sets, then P(A) u P(B) c P(A u B), where P(A) denotes the power set of A

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Q: Let A, B and C be non-empty sets and let X= (A-B)-C and Y=(A-C)-(B-C) .Check whether X=Y or not.

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Q: b) B = {(x, y) : x² < e*+3y < 5y + 4x},

A: The objective is to find the closure of the given set.

Q: Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B).…

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Q: Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered…

A: Given that: n(A)=p, and n(B)=q

Q: Give an example of sets S and T where P(SUT)メP(S) U P(T)

A: Let, S={3,7} and T={4} be any set and P(SUT) be a power set of union of S and…

Q: The intersection of sets A and B is denoted by which of the following?(a) A ∩ B (b) A ∪ B (c) A ⊆ B…

A: Sets are represented as the collection of different objects . There can be a finite set or an…

Q: For any sets A and B, show thatP ( A ∩ B ) = P ( A ) ∩ P ( B ).

A:

Q: Find the set P([a, b]) x P({0,1)).

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Q: Let A and B be two sets. (a) Show that (A°n B°)° = AU B and (AºU Bc)C = AN B. %3|

A:

Q: For any two sets A and B, if A=B,then A=B صواب ihi

A: Given a statement

Q: Let A, B, C be sets. Simplify (A∪(B∩C))∪((Bc ∩Cc)∪C)c

A:

Q: Let A, B and C be any sets. Which of the following is equal to (A U C) n (B \ C)? Select one: a. (A…

A: Solution is given below:

Q: Determine whether or not the given set is (a) open,(b) connected , and (c) simply-connected. {(x,y)…

A: Determine whether or not the given set is (a) open,(b) connected , and (c) simply-connected. {(x,y)…

Q: Let A and B be sets. Then B (B – A) -

A: Complement of set A =1-A

Q: Let A and B be sets. Then B - (B – A) AN B is equal to the above

A: Let A and B be sets  Let x∈B-B-A ⇔x∈B and x∉B-A ⇔x∈B∧x∉B∨x∈A⇔x∈B∧x∉B∨x∈B∧x∈A⇔x∈B∧x∈A⇔x∈A∩B ( since…

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”.