Q1 Let U : Determine the following. {1, 2, 3} be the universal set and let A = (1, 2}, B = (2, 3} and C = {1,3}. (a) (AUB) – (BnC) (b) Ā (c) BUC Score

Q: Prave that for all sets A and B, (ANB) = A UBC %3D

A:

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Let J={1,2,3,…}, the set of counting numbers and let R be the set of real numbers. Is R-J countable?…

A:

Q: Show that if P(A|B)> P(A), then P(B| A) > P(B).

A:

Q: Prove using the properties of set operations: a. If A and B are sets then [(A - B)c n A] C B

A: The given expression is A-BC∩A⊂B, where A and B are sets.

Q: The set {[1 -1 3], [2 3 -2], [3 2 1], [0 0 0]} spans صواب İhi

A:

Q: Define two operations + and * on A = Z × Z as follows: for (a, b) and (c, d) in A: ɔy (a, b)+(c, d)…

A: As per guidelines, we will solve first three subparts: Define two operations + and * on A=ℤ×ℤ as…

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: (b) Let U = [-5, 10] be the universal set and X=[-2,7), Y = (-1,4] and Z= (-3,6] be it's subsets.…

A: See below the answer As per bertleby guideline I have to solve only first three subparts. So for…

Q: For each part, write the set in the form [x | P(x)] (property that describes the elements of the…

A: Explained below

Q: Example 68: (R, +,.) and (Q.+,.) are fieleds. (H.W)

A: I have proved the definition of field

Q: (iv) Show that for a countable set B, m*(AUB) = m* (A).

A: Given the a set B is a countable set and the equation m*(AUB)= m*(A) to be proved.   We know that…

Q: Let A, B, C, D be sets. (a) (b) Prove that Ax (B \ C') = (A × B) \ (A × C). Prove that (A x B) n (C…

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Q: 5. Аx (В — С) %3D (А х В) — (А хС) 6. (А - В) хС %3 (АxC) — (В хС)

A: To prove the given statements.

Q: 1. (a) Let A = {k, k +1,..., k2}, for k = 1,2,3,.... Uº1 Ak - n=1 Ak (b) Find two infinite sets A…

A: Part (a):- Given that  Ak =  k, k+1, ......, k2 ,   for  k=1, 2, 3,....Find    ∪k=150 Ak - ∩k=1∞ Ak…

Q: Prove using the properties of set operations: a. ((AUB)–C)° = (A–C) – (B – C)

A: Solution

Q: Given sets X, Y and Z, use the set properties to show that (Z - x) n (z-Y)=Z-(XUY), indicate every…

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Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B) n (A x C)

A: we have to prove the lemma .

Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Cartesian product and identity

Q: Prove that A°= A - Ab.

A:

Q: Question (2) 으 (2-3)" P(군)= Let then : %3D a Determine Zo=? and ana? b) Determine the Covergance…

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Q: Prove: For all sets A, B and C, An (B-C) = (ANB) - (ANC).

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

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Q: Q3 ( Let A, B and C be sets. Show that (C – A)n (A – B) = 0, without using membership tables.

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Q: Choose the relations that are a functions A) B) D) 21- {(0, 18), (1, 14), (2, 10), (2, 6), (3, 9)}…

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Q: Q13: Prove or disprove the following: (AUB) - C = (AUC) - (BUC) where A; B; and C are sets.

A: Q13.   The given statement is false.  Counterexample :    Consider   A = { 1, 2, 3 }…

Q: Let f(a, b) = (a + b+2) + (2a + 4b + 6)x + (a +b+c)x² and set F = {f(a, b) : a, b € R}. What is the…

A: let  fa,b=a+b+2+2a+4b+6x+a+b+cx2 and set F=fa,b:a,b∈ℝ claim- to find the value of c if f1,0+f0,1∈F

Q: Check the boxes in the accompanying figures to indicate which regions should be shaded to repr (a)…

A: Solution a: Given A∩B∩Cc=A∩B∩U-C So shaded region will be

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

A:

Q: Suppose you have the following relation: R: A-A where A = (a, b, c, d, e) %3D R= ( (a, b), (a, e),…

A: Given relation is R:A->A where A={a,b,c,d,e}R={(a,b)  , (a,e) , (b,e) }determine whether it is…

Q: Use A = (3,4,7) and B = {0,1,5,8)} to find the set (ANB) U (AN B') within the universal set U = {0,…

A: A=3,4,7 and B=0,1,5,8 with universal set U=0,1,2,....,10