Exercise 3.4.4. Let A and B be non-empty families of sets. Suppose that A ⊆ B.  (1) Prove that U X∈A X ⊆ U Y∈B Y. (2) Prove that ∩ X∈A X ⊆ ∩ Y∈B Y. Exercise 3.4.5. Let I be a non-empty set, and let {Ai}i∈I and {Bi}i∈I be families of sets indexed by I. Suppose that Ai ⊆ Bi for all i ∈ I. (1) Prove that U i∈I Ai ⊆ U i∈I Bi. (2) Prove that ∩ i∈I Ai ⊆ ∩ i∈I Bi.

Q: Suppose X and Y are subsets of some universal set. De Morgan's laws provide expressions for the…

A: X∪Yc=Xc∩Yc

Q: Let X={a,b,c} and Y=∅. What is X∪Y?

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Q: R= {(a,b)|a E T,b e T, a has higher GPA than b}. Why?

A: No, it is not a poset.  Since we know that a relation is a poset if the relation is…

Q: I don't understand why you put Ui element of I. I think you made a mistake. Please let me know.…

A: Step 1:Step 2:Step 3:Step 4:

Q: Let A, B, and C be subsets of a universal set U and suppose n(U)= 150, n(A) = 22, n(B) = 24, n(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 ×…

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Q: Problem 21 For each of the following pairs of sets X and Y, compute the symmetric difference of X…

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Q: 1) Let the set S be defined as S = {x | x is a U.S. President} Find n(S). 2) Define compliment to a…

A: use the basic property of sets .

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

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Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: Exercise 1. Prove that for sets A, B,C we have C \(AUB) = (C\ A) N (C \ B).

A: We have to show that for sets A, B, C   C ∖(A∪B)=(C∖A)∩(C∖B).

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: Let U be the universal set with disjoint subsets A and​ B, where n(U) = 37​, n(A) = 8​, and n(B) =…

A: first we will find the value of n(A'∩B') we know according to De Morgan's law  A'∩B' =…

Q: Exercise 3.4.7. Let I be a non-empty set, let {Ai}i∈I be a family of sets indexed by I and let B be…

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Q: Prove that if X ∩ Y = X ∩ Z and X ∪ Y = X ∪ Z, then Y = Z for all sets X, Y , and Z.

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Q: et A, B, and X be sets. Prove that if ACB, then AnxCBnx.

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Q: Let A and B be sets. Let X = A n B, Y = A \ X and Z = B\ X. Prove that X n Y = Ø, X n Z = Ø, Y n Z =…

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Q: 9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

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Q: (b) Let={A i EN} be a family of sets with A₁ CA₂ CCA10 C... Prove that nA = A₁.

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Q: Consider following five sets: I. { , } { } II. { } III. IV. { , , } V. { , } Find all linearly…

A: We have to check whether given set of vectors linearly independent or linearly dependent by known…

Q: Let A and B be non-empty subsets of R. and let C = {2 +y: * € A,y € B}. Show that inf A+ inf B = inf…

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Q: Let A E R2x3, be R². Determine whether or not S = {x R³ | Ax=b, x₁ ≤ 0, x₂ ≤ 0} X2 sa convex set.

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Q: Choose the correct Venn diagram to represent the set XUY #XU(Ynz). D

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