Let A and B be sets. Then B- (B – A) | ANB O is equal to the above ĀNB is equal to the above None of these

Q: Let A and B be sets. Use a proof by contradiction to show that An (B – A) = 0. your proof must be by…

A: Solution a: Let's assume that A∩(B-A)≠ϕ Let  x∈A∩(B-A)⇒x∈A and x∈(B-A)

Q: Let the universal set be the set R of all real numbers and let A={x€R|-2<x<2} and B= {xeR|-3<x<0}…

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Q: Let the universal set be the set R of all real numbers and let A={x eR|-2<x<2} and B = {xe IR|-3<x <…

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Q: If C = {x:x² + 11x + 30 = 0,x E N}, then C is a/an? Finite set None of these Empty set Infinite set

A: A set which contains no element is called null set or empty set.  A set S is said to be a finite set…

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

A: Since R is universal set.

Q: For the given sets A and B, find A∩ B, A∪ B, and Ac (the complement of A). A and B are subsets of…

A: We need to find A Intersection B                               A union B…

Q: If A = {x: x |B| D. None of these {x: x 2 + 11x + 30 = 0,x E N}, then C is a/an? A. Empty set B.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Let S = (x: (x - 1)² = 0}, state where S is singleton set or not.

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Q: If C = {x: x? + 11x + 30 = 0,x € N), then C is a/an? Finite set None of these Empty set Infinite set

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Q: Let + stand for the symmetric sum of sets, A+ B = (AU B) \ (A n B). Prove or disprove (A+ B)nC =…

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Q: If A,B and C are sets, then A x (B-C) = (A × B)- (A x C). |

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Q: 1. Let A and B be two finite sets such that n(A) - 20, n(B) - 28 and n(A u B) 36, find n(A n B). а.…

A: As per guidelines we are going to solve one question

Q: Which of the following set is empty a. {x: x = x} b. { x : x != x 2 } c. { x : x ! = x } d. {x:…

A: Empty set:            The empty set is the unique set having no elements. and its cardinality is…

Q: Let A and be any sets. Mark the statement that is true OAUB CA OA - B C В В СВ O AC = { } = OANB C в

A:

Q: Find the number of proper subsets of the set. {x |x is a day of the week} O A. 256 O B. 64 O C. 127…

A: Given x | x is a day ofthe week

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

A:

Q: 4) Let A and B are two sets as given below, show that A = B. A = {m EZ| m = 2a for some integer a}…

A: The given sets are:A=m∈ℤ m=2a for some integer aB=n∈ℤn=2b-2 for some integer bWe have to show that…

Q: True or False: For sets A and B, if A cB, then A u B = A. True False

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Q: if A and B are sets, then A x B=B x A

A:

Q: The counterexample of A = {1} and B = Ø disproves which of the following statements where P(X)…

A: Given that A=1,B=∅. For (a). PA∩B=P1,∅∩∅=P∅=∅ And, P(A)∩P(B)=P1∩P(∅)=1,∅∩∅=∅ Hence statement of (a)…

Q: Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False.

A: Use the basic properties of intersection and cartesian product to prove the given relation.

Q: Define sets A and B as follows: A = {n €Z|n= 8r - 3 for some integer r} and B = {m €Z|m = 4s + 1 for…

A:

Q: Let U = {x |x is a positive integer and x <10} be the universal set, A = {x | x €U and x is a factor…

A: We have set U, where U is a universal set And A and B are sets whose elements are from U.

Q: Let A, B, and C be sets, evaluate: (A - C) n (C – B) O A O AnB O None of the choices

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Q: Let A = (-2, 4)., and B = [0, 0). Choose sets that are infinite and uncountable. O B° \ A O Bº nQ O…

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Q: Let A and B be sets. Then B - (B - A) ВПА ANB is equal to the above O is equal to the above ĀNB None…

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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: Let A and B be sets then A + B if, and only if A ¢ B or B ¢ A. 8. For sets A, B, and C, A U (B N C)…

A: True or False :  (7)  Let A and B be sets , then  A≠B if and only if  A ⊄ B or B ⊄A. (8) For sets A,…

Q: Let sets A and B be defined as follows. Bis the set of integers greater than -5 and less than 4 lW…

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Q: Let A and B be non-empty sets of real numbers with inf(B) = 2 and sup(A) = ; Then sup(2A – 3B)…

A:

Q: If A and B are any two sets and A U B = A ∩ B, then a. A= Ø b. B= Ø c. A=B d. None of these

A: topic - sets option C.   A=B

Q: Let U= {x|x is a positive integer and x <10} be the universal set, A = {x|x €U and x is a factor of…

A: A={1,2,3,4,6} B={2,4,6,8,10}

Q: A combination is a selection of r distinct objects from a. Not above b. n objects O C. r objects d.…

A: Combination:   It is nothing but the objects are being selected when the order of selection is not…

Q: If A and B are sets such that ACB then A × BC B x B. true false

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Q: (f) Let A, B and C be three sets. Prove by contradiction that if An BC C and r E B, then x ¢ A - C.

A: Let A, B and C be the three sets. Prove that, A∩B⊆C, and x∈B, then x∉A-C

Q: if A and B are set, then A x B=B x A  True or False

A:

Q: Let the universal set be the set R , and let A={xER| 0≤ x <4 } B= {XER| 2<x≤10} Find  a. B-A  b.…

A: Given A= { x ∈R :0≤ x &lt;4 }, B= {X∈R : 2&lt;x≤10} Given universal set be the set R.

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: Let A and B be sets with A ⊆ B and B transitive. Prove each of the following: 1. P(A) ⊆ P(B). 2.…

A: It is given that the set A is a subset of the set B. First we have to show that PA is a subset of PB…

Q: If A and B are sets, then P(A) U P(B) = P(A U B). Select one: o True o False

A:

Q: If n(A ∪ B) = 2n(A), then A and B are equivalent sets.

A: Here use definition of equivalent set

Q: Let A. B. and C be non-empty sets. Then A B C=C×B×A if and only if* O B=C O None of these O A=C O…

A: Let us consider four non empty sets A, B, C and D such that A x B=C x D if and only if A=C and  B=D…

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: List the elements ot Hhe Sets in a-h A) AnB B) Bnc c) Anc D) ANBAC E) AUB +) B UC f) BUC G) AUC H) A…

A:

Q: Let A and B be sets. Then A - (Ā – B) BN A is equal to the above None of these ĀNB is equal to the…

A: The objective is to choose the correct representation of A-A-B

Q: Define sets A and B as follows: A = {a € Z| a = 8m - 3 for some integer m} B = {b € Za = 4n + 1 for…

A: Given that A=a∈Z|a=8m-3 for some integer m. B=a∈Z|a=4n+1 for some integer n. let a∈A  therefore…

Q: Q2. Is it TRUE that for all sets A and B the identity below holds? A\(A\ B) = ANB

A:

Q: a) Let the universal set be the real numbers R and let A {x €R|2< x <7} and B = {x ER | 1 < x < 5}.…

A: First we find intersection then find compliment

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”.