For every two sets A and B, if A–B = B – A , then A-B=Ø. For every two sets A and B, ANBCA-B.

Q: b) BCA iff A n B = ¢ c) (A – B) U B = A iff B C A

A:

Q: For any sets A and B , (ANB) = %3D O a. ANB O b. ANB Oc. B-A С. В- А O d. U-B

A: By using identities of set theory :

Q: For sets A and B, prove that AU (B – A) = B

A:

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

A: Since R is universal set.

Q: State whether or not each of the following sets is closed under the operations of addition and…

A:

Q: , B, and C which satis

A: Given as, A= {1, |B|, |C|} B= {2,| A|, |C|} C= {1, 2, |A|, |B|}

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 10}.  (Enter your answers as a…

A:

Q: Find the complement of the set given that U = {x | x I and −3 ≤ x ≤ 9}. (Enter your answers as a…

A: First we write U and the set in roaster form.

Q: Write each of the following sets in the form of listing its elements (i.e. in the form {a,b,c} to…

A: 1). A set ∅ is known as an Empty Set (i.e., a set having no elements). Here P({∅}) is the power set…

Q: Indicate whether the following sets are equal. A={x, j, a, w}, D={x, a, b, y}

A: The given two sets are, A=x,j,a,w and D=x,a,b,y By definition, The two sets A and B are equal sets…

Q: Define E to be the empty set and further define F = {E}, G = {F}, H = {E, F}, and I = {E, F, G,H}.…

A:

Q: For any sets A, B, and C, prove that Ac Bnc if and only if A c B and A CC

A: Consider the statement,

Q: Consider the following statement. For all sets A and B, (A U B)C = A©U B°. Which sentence below…

A:

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

A:

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: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: Complement: The complement of a set A is the set of elements in the universal set U that are not in…

Q: If A and B are sets; Aºand Bºdenote the complements of the sets A and B, then the set (A – B) U (B –…

A: Given:- If A and B are sets; Ac and Bc denote the complements of the sets A and B, then the set (A -…

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

A:

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

A:

Q: For any sets A, B, and C; the distributive law states AU (B n C); that is a. (A U B) n (A U C) c. (A…

A: DeMogran's distributive law

Q: simplify each of the following sets and state whether the set is finite, countably infinite or…

A:

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

A: The Venn diagram for 2 sets can be drawn as follows.

Q: Disprove: For all sets A, B, C, and D, (AUC) × (BUD) C (A × B) U (C × D).

A:

Q: Find

A: First we write U as universal set. Then find complement.

Q: . If each element of a set A is also an element of a set B, we say that A is a_____ of B and write A…

A: A set is a collection of objects such that no object can be repeated. Two sets can be compared to…

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 9}. (Enter your answers as a…

A: First write U and the given set in roster form.

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 7}.  (Enter your answers as a…

A:

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 10}.  (Enter your answers as a…

A:

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

A: For sets A, B and C, prove that (A∩B) x C = (A x C)∩(B x C).

Q: If X and Y are two sets such that           n ( X ) = 17, n ( Y ) = 23 and                    n ( X…

A:

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

A:

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: First we write U in roster form.

Q: Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B).…

A:

Q: the set A = {=: (ne Q)^(n > 0)}; 3(0 )v(d au):-

A: given set A=1n:n∈ℚ∧n>0 Determine whether the following set is well-ordered:

Q: Which of the following statements is true OA. For all sets A, B and C, A- (B –C) = (A - B) -C- O B.…

A: Option B and E are correct.

Q: Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered…

A: Given that: n(A)=p, and n(B)=q

Q: Give an example of sets S and T where P(SUT)メP(S) U P(T)

A: Let, S={3,7} and T={4} be any set and P(SUT) be a power set of union of S and…

Q: For any sets A  B, C, ( A ∩ B) ∪ C ≠ A ∩ ( B

A: Given that the sets A, B, C. Consider, A∩B∪C=A∪C∩B∪C.............(1) Consider,…

Q: Which of the following statements is true OA For all sets A, B and C. if AUC=BUC then A =B. O B. For…

A:

Q: For every set A, {Ø} C A.

A: We use the definition of an empty set and subset of a set to answer the given question.

Q: For any sets A and B, show thatP ( A ∩ B ) = P ( A ) ∩ P ( B ).

A:

Q: Find the cardinal number for the set. B= {x | xEN and 6<x<8) n(B)%= !!

A: To find the cardinal number of the given set B .

Q: For two sets Aand B, prove the following: a. An Bº, Aº n B, and A n B, are mutually disjoint. b. A =…

A: Note: Hey there! Thank you for the question. As you have posted multiple sub-parts, we have helped…

Q: Let A, B and C be any sets. Which of the following is equal to (A U C) n (B \ C)? Select one: a. (A…

A: Solution is given below:

Q: Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1)are in A × B, find…

A: In AxB the first element will be from A and the second element will be from B So, x,y,z are in A And…

Q: If A and B be measurable sets, ACn BC is measurable.

A:

Q: For the sets A = {x | x &lt;= 9, x is a natural number}, B = {2, 4, 6}, C = {3, 5, 8, 10}:a. Which…

A: Here given set A=x|x≤9, x is a natural number=1, 2, 3, 4, 5, 6, 7, 8, 9 and B = {2, 4, 6}, C = {3,…

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”.