Let A. B. and C be non-empty sets. Then AXBXC=C×B×A if and only if* O B=C None of these A-C A-B3DC O A=B

Q: Let 4, B, and C be sets. Show that а) (А — В) — С СA-C. b) (A — C) n (С- В) — 0.

A: It can be solved by the set theory

Q: Prove: If A,B and C are sets, then A ×(B ∪C) = (A ×B)∪(A ×C).

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 A, B and C be sets. Use an element argument to prove the following. (A - B) n (B-A) = 0.

A:

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

A:

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

A:

Q: Determine whether the set S = {1, x², 3 + x²} spans P2. O S spans P2. O s does not span P2.

A: Consider the given set S. S=1,x2,3+x2 Now, make the matrix from the given set. 103000011

Q: Prove : a. For any sets A and B, AXB=BXA b.For any sets A, B, C (A x B) x C Ax B x C AX (BXC) c. If…

A: let the set A and B are A= ( m,n)   , B = (n,m) Now, A×B = {(m,n), (n,n),(n,m),(m,m)} B×A=…

Q: Let A, B be any sets with ACB. Then* |P(B × B)| > |P(Ā × B)| O None of these the above is true |P(A…

A:

Q: Prove that for sets  A and B,  we have  (A∪B)−(A∩B)=A−B if and only if B⊂A.

A: By theorem we know that,            A⊂B if and only if A∩B =A and  A∪B =B

Q: If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

A: Let us understand it by and example,   Let, A={1,2,3} and B={1,2,3,4,5} Here we can see that A ⊂ B

Q: Let A and B be sets. Prove that A c B if and only if A NB = A.

A:

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

A: True.

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

A: We can tackle this problem easily by assuming some examples  case (i) Let A=B=C = {1,2} we have,…

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

A:

Q: If sup A < inf B for sets A and B, then there exists a c€R satisfying a <c<b for all a EA and bEB.

A:

Q: Let A, B, and C be sets. Prove A × (BnC) = (A × B)n (A × C).

A:

Q: Let A, B be any sets with ACB. Then O None of these O IP(BxB)|s|P(A×B)| O IP(A×B)=|P(B×B) O…

A:

Q: 2. Let A, B, and C be sets. with (A - B)nC the empty set. Prove that AnC C B.

A: Recall the following. A-B=A∩BcIf x∈A⇒x∈B, then A⊂B

Q: Let A = {2n : n e N}, and B = {n E Z : n² is even}. Neither set is a subset of the other. O AC B. O…

A:

Q: Suppose A and B are sets. Prove that A – B = AN B.

A:

Q: b) BC A' iff A o B = ¢

A: Solution is given below:

Q: If A and B are sets, then A n (B – A) = Ø. %3D

A:

Q: For any two sets A and B, if m* (A) = 0, then m* (AUB) = m* (B). In particular, if BCA, then m* (B)…

A:

Q: If A and B are any two sets and AUB = . A n B, then

A:

Q: If A and B are sets and A is a subset of B, then A and B cannot be disjoint.

A:

Q: Show that if A and B are sets with A ⊆ B, then a) A ∪ B = B. b) A ∩ B = A.

A:

Q: If C {x: x2 + 11x + 30 0, x e N}, then C is a/an? %3D Infinite set Finite set None of these Empty…

A: We have to find the set C

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

A:

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

A:

Q: 4. Let A and B be any two non-empty sets. Prove that P(ANB) = P(A)NP(B).

A:

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

A:

Q: If A, B and C are sets such that; A ∆ B = A ∆ C, then   B is a subset of C        Select one: A.…

A: The meaning of A ∆ B is A ∆ B = (A u B) - (A n B) So A ∆ B contains that elements from set A and set…

Q: Show that if A and B are sets, then P(A) u P(B) C P(A u B), where P(A) denotes the power set of A

A: For a set A, the set of all its subsets is called the power set of A. Now, consider two sets A and…

Q: Show that if A and B are sets, then P(A) u P(B) c P(A u B), where P(A) denotes the power set of A

A:

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: 2. Determine if the following statements are true or false. Here A represents any set. (a) ¢ C A (b)…

A: Used simple logic to prove.

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 D be sets. If A n B = Ø then prove that (A – B) – (B n D) = A.

A: Take x in left hand side and prove it belong to A and vice versa.

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

A: B=C

Q: Let A and B be sets. Prove that PLA) O P(B) = P(AO B

A: Introduction: The union of any two or more sets yields a fully new set that comprises a mixture of…

Q: For any two sets A and B, if A=B,then A=B صواب ihi

A: Given a statement

Q: (4.1) For sets A and B. prove that P(AB) = P(A)~P(B).

A:

Q: Let A and B be sets. Then B (B – A) -

A: Complement of set A =1-A

Q: Let A and B be sets. Then B - (B – A) AN B is equal to the above

A: Let A and B be sets  Let x∈B-B-A ⇔x∈B and x∉B-A ⇔x∈B∧x∉B∨x∈A⇔x∈B∧x∉B∨x∈B∧x∈A⇔x∈B∧x∈A⇔x∈A∩B ( since…

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”.