2. Exactly one of the following statements is true for all sets A, B,C. Draw a Venn diagram for the correct statement and prove it. A \ (BNC) = (A \ B)n (A \ C) A\ (BNC) = (A\ B) U (A \ C)

Q: . If A and B are sets in a universal set U, then AUB=AnB.

A: We proved this by wave diagram

Q: Which of the following set is consistent? Select one: O i. None of these O i. (A&~(BVA)} O i. (/ ) >…

A: Option 4 ) { A ⊃ B , B ⊃ C , A ⊃ C }  is correct

Q: - For all sets A, B and C. Is (An B) U C =An (Bu C)? Justify your statement. You may ju

A: Yes, the above statement is false and the proof of above statement is given below:

Q: (BOC)=(A-B)u(A-C). 11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A, B and C are…

A: Please refer to the solution in next step.

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

A: Example of such set A,B,C,D are given below

Q: O ACBiff P(A) C P(B). O ACBIF and only if AU B= B (A x B) U (C x D) (AUC) x (BU D)

A:

Q: Prove that {9":ne Q} = {3":neQ}.

A: Two sets A and B are equal i.e. A=B if and only if

Q: . If A and B are sets in a universal set U, then AUB=AnB. A-(BnC)=(A-B)U(A-C). . If A, B and C are…

A:

Q: 3. Let A and B be two sets. Use set operation properties to prove the identity ,AÐB = AUBU (AO B).

A: To prove the identity

Q: 15. If A, B and C are sets, then (AnB)-C=(A-C)n(B-C). m

A:

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

A: The detailed solution is as follows below:

Q: Let A, B, and C be subsets of a set S. Prove the following statements and illustrate them with…

A: As per the question we are given three arbitrary subsets A, B and C of a set S. And we have to prove…

Q: Which of the following set is consistent? Select one: O i. None of these O ii. (A&~(BVA) } O i. {J>…

A:

Q: Sets B and C are subsets of the universal set U. These sets are defined as follows. U={f,k,m, x,y }…

A: It is given that: U=f,k,m,x,y,B=k,y,C=f,k,m Therefore the complementary sets of B and C are:…

Q: 10. Place the correct symbol from the list C, =, 2 between each pair of sets below a) AUB, AU (B −…

A: A set is a clearly defined set of unique elements in mathematics and computer science. These…

Q: Let U be a universal set and A, B, C CU. ITEM 1. Prove: A n BCAUB

A: # as per the guidelines we are entitled to solve one question at a time please resubmit the other…

Q: Let A and B be sets. Prove that Ac B if and only if AnB = A.

A:

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Describe the following sets in words and/or pictures: 1. {(x,y,z): y = x2 } 2. {(x,y,z): y > z }…

A: Here, to describe the given sets in words and/or picture.

Q: The market research department of an electronics company has determined that the demand and cost…

A: Cost function is given by: C(x)=2250+5x Now, put x=300-5p C(x)=2250+5(300-5p)       =2250+1500-25p…

Q: What is (A∪B)c where A={5,11,3,8,9} , B={99,5,11,2,4} and Universal Set…

A:

Q: Q3: Let A,B, C , be sets with a universal set U. Please draw and express with pictures each of the…

A:

Q: 2. Prove or disprove each of the following statements, for any three sets A, B, and C: a. (ANC) -…

A:

Q: Use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.…

A:

Q: Find the glb and lub of the following sets. Which of these belc A = 72 n+1

A:

Q: (BOC)=(A-B)u(A-C). 11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A, B and C are…

A: To prove the equality A - (B ∩ C) = (A - B) ∪ (A - C), we need to show that each set is a subset of…

Q: 17. If A,B and C are sets, then Ax (BnC) = (A x B) n(A x C).

A:

Q: 18. If A,B and C are sets, then Ax (B-C)= (A x B)-(AXC).

A: By the using of definition we prove this.

Q: 4. Let A and B be sets in a universe U. Consider the following two statements: i. P(AU B) ii. P(An…

A:

Q: Let U= { 1,2,3,...,20}. Let A, B, C be the subsets of U. Let A be the set of all numbers, which are…

A:

Q: 14. If A,B and C are sets, then (AUB)-C=(A-C)u(B-C).

A: To prove the equality (A∪B)-C = (A-C)∪(B-C), we need to show that any element x belongs to the…

Q: et the domain be the set of all people. Let: P(x, y): x knows y. Vhich of the following is the…

A: Here we use predicate logic

Q: Prove: If A, B and C are sets then AU(BOC) and ((C- (AUB)) (B- (AUC))) are disjoint sets.

A: Let A, B, and C are sets. Now we prove that A∪B∩C and C-A∪B∪(B-(A∪C)) are disjoint.

Q: 16. If A, B and C are sets, then Ax (BUC)= (A x B)U(AXC).

A:

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”.