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.

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: Which of the following are difference sets?

A: Introduction: A (v, k, λ) difference set is a k-element subset D of V = Z (mod v) in which any…

Q: Consider the following sets: A = {x | x ∈ N and x > 2} B = {x | x > 2} (a) Write a description of…

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Q: For Exercise, write the set as a single interval. [(-, -2) U (4, o)]N (-5, 3)

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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: Vhich of the following sets is a null set ? I. X {x | x= 9, 2x = 4 } II. Y {x | x= 2x, x #0 } III.…

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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: Define two sets, call them A and B, that makes the following statement true; if it is impossible to…

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

A: Since R is universal set.

Q: Determine the domain and range of the following relations using set builder notation. а. b. 2. 3 1 2…

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Q: What is the intersection of sets A and B?

A: The intersection of sets is a set which include the common of the two sets A and B. It is…

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Let A, B, and C be sets. Is the following equality true or false? A x (BUC) = (A × B) U (A × C')

A: Sets, distributive law

Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if*

A: Let us consider four set A , B, C and D then AxC=BxD if all the elements of A are same as all the…

Q: Simplify the set expression (X∩Y’) ∪ (X∩Y)~X’ using the Laws on Sets.

A: (X∩Y') ∪ (X∩Y)=(X∩Y') ∪ X ∩ (X∩Y') ∪ Y  distributive property, A∪(B∩C)=A∪B∩(A∪C)=X∩ (X∩Y') ∪ Y…

Q: Let the following sets A, B, and C be finite sets with|A|= 6, |B| = 8, |C| = 6, |A ∪ B ∪ C| = 11, |A…

A: Let the following sets A, B, and C be finite sets with|A|= 6, |B| = 8, |C| = 6, |A ∪ B ∪ C| = 11, |A…

Q: The boundary of a set is equal to the boundary of the complement) True or false

A: (The boundary of a set is equal to the boundary of the complement) True or false

Q: Create three non-empty sets A, B, C, that show this statement is FALSE: For all sets A, B, C: A- (Bn…

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Q: If A = {(x, y): (2, -2), (4, -1), (6, 0), . . .}, complete the rule for set A. y= 1/2x - 3 -1/2x -…

A: Observe the given pattern of set A then complete the rule.

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

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Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if

A: A, B, C are three non empty sets,  And, it is given that A × B × C = A × C × B

Q: b) By using the laws of set theory, show that [(A U B) n (An C)] u (B n C) = A U B.

A: Here we have to prove left hand side is equivalent to right hand side using laws of set theory

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, B, U and V be any sets such that A⊆U and B⊆V. Is (A×B)⊆(U×V)? Justify your answer

A: In the given question we have to justify that, is the set A×B⊆U×V where A⊆U and B⊆V. for the…

Q: R, S and T are closed sets implies RnSnT is closed.

A: given

Q: Describe the following sets in words and/or pictures: 1. {(x,y,z): y = x2 } 2. {(x,y,z): y > z }…

A: Here, to describe the given sets in words and/or picture.

Q: If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10…

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Q: Find the intersection of the sets. {a, b, c, d}∩∅

A: Given sets are {a, b, c, d} and an empty set ϕ

Q: ) Suppose X = {1,2, 3} and Y = {5,6). The number of elements of the set P(X × Y) = %3D

A: Number of Elements in Power Set P(A) of set A with n elements is 2n

Q: The empty set is open set

A: See the detailed solution below.

Q: If X and Y are two sets such that           n ( X ) = 17, n ( Y ) = 23 and                    n ( X…

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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: Decide whether the statement is true or false. Two set A and B are equal if have the same number of…

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Q: Define the sets A, B, C, and D as follows: A = {-3, 0, 1, 4, 17} B = {-12, -5, 1, 4, 6} C= {x € Z: x…

A: Intersection collect all common elements and in union collect all elements

Q: If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements,…

A: Given that n(X ∪ Y)= 50  n(X)= 28 and n(Y)=32  We have to find n(X ∩ Y )= ?

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

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Q: If X and Y are two sets, then X∩(Y∩X)c equals a. Ø b. Y c. X d. X∩Yc

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Q: If A and B are two sets satisfying A∖B=B∖A what can we conclude about A and B? Explain.

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

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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 finite sets with |A|=10, |B|=5, |A∪B|=12 what is |A∩B|?

A: Given,  |A|=10 |B|=5 |A∪B|=12 |A∩B|=?

Q: For any sets A  B, C, ( A ∩ B) ∪ C ≠ A ∩ ( B ∪ C). True or False.

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Q: Let A and B be sets. Then B - (B - A) ANB is equal to the above Ā NB is equal to the above

A: Here ,we are given that A and B are two sets. We need to find  B-(B-A) : Now, Here ( B-A) represents…

Q: Write the set X = {... -1, -0.9, -4/5,-0.7, -3/5, -1/2, -2/5, -0.3, -1/5, -0.1 0,0.1, 1/5, ...} in…

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Q: List all the ordered pairs in the relation R= {(a, b) | gcd(a,b) = 1} on the set {2, 3, 4, 5, 6}.

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