TION 4 If A, B, C be three sets such that Au B = AUC and ANB = ANC, then : O B = C O A = C O A = B = C O A = B O None of above

Q: 5. For the set C = {4, 5, 6, ....} is it true or %3D false that 7 e C? True False

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are two sets. find R = {(x, y): x EX and y EY and (y * –…

A: R has three elements.

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: Queston2 {e-x, xe-O onlo, c∞) a) shau that q fandamented Set

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Q: Prove or disprove: For all sets A and B, An(AUB)

A: We have to prove or disprove , for all sets A and B A∩(A∪B)=A.

Q: Let A={1,2,3,4,5} and B={2,3,4}. Find C such that CCA and BC. (There are more than one possible sets…

A: A set is a collection of objects. A set has the property that elements in the set cannot be…

Q: 2. If A = {a,b,c}, B = {1,2,3}, C = {x}, and D = 0, list all of th the following sets. (a) Ax B (c)…

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Q: Example 5. If A, B and C are three sets and U is the universal set such that n(U) = 1000, n(A) =…

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Q: (a) Give an example of sets A and B such that (An B)° # A°NB°.[ (b) Prove that for all sets A and B,…

A: a) give an exapmle of sets A and B such that (A∩B)c#Ac∩Bclet A=Q (set of rational numbers)…

Q: 4. Prove or disprove For all sets A. B and C. if A OC-0,then A. B and Care your answers as ar AUD,…

A: The given statement is FALSE.

Q: Let A be a pnuta set and let 1OCA>I = n. det B=AU{z} for some x4B, how dou B many hame. Why? Sulret

A: Given: pA=n  B=A∪x for some x∉B Therefore, ⇒pB=n+1 We know that, If there is an n element in a set…

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: If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements andY has 15 elements ; how…

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Q: 1) Prove that AU(Bnc)= (AUC)N(AUC) 2)Let M-{1,3,n}, find the power set of set M

A: Find the attachment

Q: (b) Prove that for all sets A and B, (AN B)° = A¢ U B°.

A: We have to prove that for all sets A and B, A∩Bc=Ac∪Bc

Q: 6. Let A, B be finite sets. Show that if JA\ B| = |B\ AJ, then |A| = |B|.

A: The order of a set defines the number of elements of the set. For two finite sets A and B,…

Q: Which of the following sets is (are) proper subsets(s) of the set of the multiples of 5? Choose one…

A:

Q: Which sets are compact? The union of [0, 1] and [2, 3]

A: Concepts introduction: Theorem (Heine-Borel Theorem): A subset S of R is compact if and only if S is…

Q: For R", { (1,1,0, 4) , (1, 0, 1,0), (-2, 3, 1, 4), (2,1, -1, 1) } A Does A set form a bose for R"=?…

A: Take A=11-221031011-1-1041 Apply the row operations to reduce the matrix to echelon form.…

Q: Which of these are sets having the 2nd element as the inverse of the 1st element? A. (D,A) and…

A: Use the definition of identity and inverse element.

Q: 4) Using equality of sets, prove that (An B)' = A' U B'

A: we know thatA∪B=x: x∈A or x∈BA∩B=x: x∈A or x∈BA'=x:x∈U, x∉A=U \ AWhere U is a universal set.That is…

Q: Suppose A and B are two sets such that ANB = Ø. Which of the following statements is/are true? (i)…

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Q: Let A = {1,2,3,4,5,6}, how many different relations are there on a set A?

A: First, we need to know definition  of the Cartesian Product of a set is with itself. The Cartesian…

Q: 5. Give an example of a collection (A,, of sets with the properties that: (a) A, # Ø for each i> 1,…

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Q: şa,6şc2.Debine a selation I on. pl2) which satisfies. For all set A and B in P(X) AJB ANB+

A: Given x={a, b, c}P(x)={ {a} , {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}, ∅}a relation onJ: P(x)…

Q: Let R, S, T be subsets of the universal set U such that n(U) = 64, n(R U S U T) = 45, n(R) = 22,…

A: We will draw a Venn diagram using the given information: n(U) = 64, n(R U S U T) = 45, n(R) = 22,…

Q: 1.         Consider the sets: A = {a, b, c, d, e, f, h, j}, B = {a, b, i }, C = {f, h} and U =…

A: From the given information, the given sets are:

Q: 8. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A: Define A={1,2} and B={1}.

Q: 4. Let the universal set U = {0, 3, 4, 6, 7, 8, 9, 10} If A = {3, 6, 9} and B = {4, 8}, find the…

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Q: Let A and B be finite sets satisfying |A| = 6, |B| = 7 and |AN B| = 2. %3D Calculate the following:…

A: # we are entitled to solve three subparts at a time, please resubmit the other parts if you wish to…

Q: Find an example of sets A and B such that |A|=3,|A|=3, |B|=4,|B|=4, and |A∪B|=5.

A: Let A = {2, 3, 4} and |A|= 3 and B = {2, 4, 6, 8} and |B|= 4 The union of set A and B is the set of…

Q: List the elements of set D = { x:x є N, x is a multiple of 5} where N= {1, 2, 3, ...}.

A:

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: Let A={2,4,6,...}, then A is well-ordered set ylgn ihi

A: Given a statement

Q: A Partition of a set has 3 subsets: A, B, and C. If Pr[A]=.25 and Pr[B]=.45, find Pr[C].

A: The provided information is,P(A) = 0.25P(B) = 0.45According to the general law of probability, the…

Q: The set {(a,b) : a EA and b EB} denoted by ...............

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Q: 12. Find two sets A and B such that A e B and A B.

A: 12.Find two sets A and B such that A∈B and A⊑B

Q: Let X and Y be the number of tables and chairs in an office. p(x, y) of X and Y is given in the…

A: From the given information, the joint density for X and Y is,   y=0 y=1 y=2 y=3 x=1 0.05 0.06…

Q: 1. Decide whether the folloring stabe ments ae false . Justify true or (a) YxeTR, ¥yeR, x²-y² z xy…

A: 1. a ∀ x ∈  R, ∀ x ∈  R, x2+y2 ≥ 2xy  TRUE. Because,  ∀ x ∈  R, and ∀ x ∈  R we have (x-y)2 ≥ 0.…

Q: Let A = [3, 8], and B= (-00, 4). Choose sets that are infinite and uncountable. O P(ANN) O P(AnQ) O…

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Q: (i) If A and B are two sets such that ACB, then m* (A) ≤m* (B).

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Q: Express the set in roster form. B= {x| xEN and x is even) Choose the correct answer below. O A. B=…

A: Please refer the attached image for complete solution.

Q: 7. Let A, B CR be the sets (-∞, –1) U [0, 1)U [2, ∞) and B = [-2,0.5) U [0.5, 4]. Write down the…

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Q: 2. Let U = {a, b, c, d, e, f, g, h} be the universal set, and let A = {b, c, d, f, g}, B = {a, b,…

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Q: Consider the following: Let the universe of A and B be the set U. An B= AUBIF and only if A = B. A…

A: Solution by using properties of sets :

Q: d) Let X, Y, Z be sets. Calculate |X UYU Z| if |X| = 50, |Y| = 90, |Z| = 71, |X n Y| = 8, |Xn Z| =…

A: Given that X, Y and Z be the three sets.

Q: 3A, B E {sets} such that A CBAA= B.

A: To check whether the given statement true or false: ∃A,B∈sets such that A⊆B∧A=B

Q: Let S = {1, 2, ..., 10}, A = {1, 3, 5}, B = {1, 4, 6}, and C = {2, 5, 7}. %3D Which of the following…

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Q: Prove (((LOM)-N) U(N-(LUM))) < (LU (MUN)) L, M, N are sets.

A: To prove: L∩M-N∪N-L∪M⊂L∪M∪N

Q: Let A = {H, T} be the set of outcomes when a coin is tossed, and let B = {1, 2, 3, 4, 5, 6} be the…

A: