Consider sets A={1,3,5} and B = {2,4,6}. find A ∩  B

Q: Show that the set S = {(1, 2, 3), (0, 1, 2), (−2, 0, 1)} spans R3.

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Q: 2. Find sets A, B, C, D such that the sets (AN B)U (C\ D), ((An B) U C) \ D, An(BUC) \ D, An(BU(C\…

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Q: For sets A and B, prove that P(A∩B) = P(A)∩P(B).

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Q: Consider two sets in ℝ² with the usual topology. Is the closure of a path-connected set also…

A: We will use knowledge of general topology to solve both the parts of this question. For the first,…

Q: Prove that for sets A and B, if A C B then P(A) C P(B

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Q: Let A and B be two sets with a finite number of elements. Show that the number of elements in An B…

A: Given A and B are two finite sets. To show that the number of elements in A∩B plus the number of…

Q: Let A, B and C be overlapping sets, verify following by using Venn diagram and membership table ((An…

A: Consider the provided question,

Q: For all sets A B and c, of CAXC)- CBrC)# Ø, then A-B#¢.

A:

Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

Q: Show that for all sets A, B and C, If A CB, then B CA.

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Q: S. is Setl

A: A small block slides without friction down an inclined plane starting from rest. Let sn be the…

Q: Use the Venn diagram shown to the right to determine whether the given sets are equal for all sets A…

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Q: The set of elements common to both set A and set B is called the______ of sets A and B, and is…

A:

Q: The set of elements common to both set A and set B is called the of sets A and B, and is symbolized…

A: The set of elements common to both set A and set B is called the ________ of sets A and B, and is…

Q: For an element to be in the intersection of sets A and B, the element must be in set Am in set B.…

A: Any elements of A intersection B must be in set A and in set B

Q: Use Venn diagram to shade in region of following sets: a) An(BUT) b)

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Q: For any sets A, B, show that (A \ B)c = Ac ∪ B.

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Q: (а) An B 3 o (Ъ) в СА (с) АДВ — AU B.

A: The detailed solution is as follows below:

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: 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 any sets A, B,C prove that if BCC then A – (BUC) = A – C. -

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Q: Given the sets A, B and the universal set U, and that A and B are not disjoint, draw a Venn diagram…

A: It is provided that A, B are two sets that are not disjoint and U is the universal set. We need to…

Q: The symmetric difference of sets A and B, consists of those elements which belong to A or B but not…

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Q: (4) Prove by contradiction, for any sets A and B, if ACA- B, then An B= Ø

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Q: Suppose that A, B, and C are sets such that A ⊕ C = B ⊕ C. Must it be the case that A = B?

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Q: Let A, B,C be three sets. Show that if BC A and C C A \ B, then BC A \ C.

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Q: Draw figures showing two sets A and B, so that B C A. DO NOT draw the set elements.

A: As we know the meaning of B ⊆ A is that B has few or all elements equal to the set A B ⊆ A subset…

Q: Refer to the following Venn diagram, and list the points that belong to each set. (Enter your answer…

A: Consider the given Venn diagram, which is given in the question. From the Venn diagram…

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: Show by membership that for all sets A, B and C: А - (AnB) CА - В

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Q: Prove by contradiction, for any sets A and B , if A CA- B, then An B = Ø

A: We want to prove if  A ⊂ A - B, then A ∩ B = ∅

Q: For any sets A and B, (AU B)

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Q: Given two sets: A = {a, b} B = {b, c, d} Construct the disjoint union of A and B.

A: Procedure to find disjoint union of family of sets. Consider family of set is  Ai:i∈ℕ∪0 . Let A=⊔Ai…

Q: For the sets U,A,and B, construct a Venn diagram and place the elements in the proper regions.  U=…

A: Solution-: We have, We construct a Venn diagram and place the elements in the proper regions.

Q: Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C?. If not, give an example.

A: No, it is not true. EXAMPLE- Let A= {2}  B= {{2},3,4} C={{2},3,4,5,6} We can see here that,

Q: Draw a Venn diagram for the symmetric difference of the sets A and B.

A:

Q: Let A, B, and C be three sets. If A⊕C=B⊕C, show that A=B

A: Solution : Given that A,B and C are three sets. And the Direct sum of set A and C is equals to…

Q: Given the following sets X= {a,b,c} Y= {a} Z= {a,d} In the universe U= {a,b,c,d,e}, what is (X’…

A: Sample Space (SS): The total number of possible outcomes of an event is called Sample Space and it…

Q: Consider sets A={1,3,5} and B = {2,4,6}. Find A U B

A: The given sets are A={1,3,5} and B = {2,4,6}. The union of any two sets is the set of all the…

Q: For any sets A and B, (AUB) = A' NB'.

A: For any two sets 'A' and 'B' A∪B'=A'∩B' In order to prove equality we will show: (A∪B)'⊂A'∩B'…

Q: is the set [5,100] compact?

A: Given that:A set is S=5,100.We have to check whether a set 5,100 is compact or not?

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: Show that if A and B are sets |A| = |B|, then |P(A)| = |P(B)|

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Q: for any sets A and B (AUB)'=A'nB'

A: We prove that for any sets A and B (AUB)'=A'nB'.

Q: Which regions represent set ANC?

A: Here use basic of venn diagram  Here in venn diagram  there are 3 events A , B and C

Q: For an element to be in the union of sets A and B, the element must be in set A in set B. but not…

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Q: Complete the membership table to show that for all sets A, B: B = (ĀU B) – B A B 11 1 0 0 1

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Q: Let A, B, C be three sets. Show that if B C A and C C A \ B, then BC A \C.

A: Given: Let A, B, C be three sets. To show: If B⊆A and C⊆A \ B, then B⊆A \ C.

Q: For any set AcR, A is a Borel set.

A: Hi! As per norms, we will be answering the first question. IF you need an answer to others then…

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”.