Exercise 3.4.7. Let I be a non-empty set, let {Ai}i∈I be a family of sets indexed by I and let B be a set. (1) Prove that B×(U i∈I Ai) = U i∈I(B×Ai). (2) Prove that B×(∩ i∈I Ai) = ∩ i∈I(B×Ai).

Q: Let A, B be set with A non-empty. (a) Prove that if A C B, then A, B are not disjoint. (b) What if…

A:

Q: Let X={a,b,c} and Y=∅. What is X∪Y?

A:

Q: R= {(a,b)|a E T,b e T, a has higher GPA than b}. Why?

A: No, it is not a poset.  Since we know that a relation is a poset if the relation is…

Q: 4: Ex 4.) Let S be a non empty bounded set in R. a ( a. Let azo, and let oS := {as: SES}. Prove that…

A:

Q: Question: 7. Suppose A and B are sets in universe U. Prove that An (AUB) = B\ A.

A:

Q: Let U be a universe and let A, B, C, D be any subsets of U. Prove or disprove the following…

A: Given U be a universe and let A, B, C, D be any subsets of U. We have to prove or disprove the…

Q: Prove: For all sets A, B and C, (AUB) - (CA) = AU (B-C).

A:

Q: If ACB then (UNA)U(BNA)=B. TO نقطة واحدة If X = (A, A, = (-1- i,1+i), iEN }, then nA = empty set. F…

A: 1 If A⊆B. Check whether U∩A∪B∩A=B Take LHS  U∩A∪B∩A=A∪B∩A    ∵[A⊆U]=A∪A          ∵[A⊆B]=A The…

Q: a) Show that the set S = {(1, 2, 3), (0, 1, 2), (– 2, 0, 1)} spans R³. b) Determine whether the set…

A: See the attachment.

Q: Prove that P(A) NP(B) = P(ANB), where A and B are arbitrary sets

A:

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Suppose that X is a set and {A. : a E I} is an indexed family of sets (which contains at least one…

A:

Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

A:

Q: Let U {1,2,..., 100}, and let A consist of 15 unknown numbers taken ran- %3D domly from U. Let B…

A:

Q: E. Show that both R and R² may be covered by countably many open balls.

A:

Q: A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A N B)…

A:

Q: 3. Let A = {a} be a bounded subset of R. Which of these three statements about A is/are not true? I:…

A:

Q: Let A and B be nonempty sets. Prove that A x B = B x A if and only if A = B.

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: Choose the best option that answers each problem. You may choose only one. 1) Let R be the set of…

A: To Choose : The best option that answers each problem.Let R be the set of all subsets of a set X.…

Q: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: Suppose F and G are families of sets. Prove that (UF)n (UG) ≤ U(F N G) iff VA EFVBE G(An BCU (FNG)).

A:

Q: 2) Explain how you count the number of elements in the set A = {n EN| n <500 and gcd (n, M) = 1},…

A:

Q: Let A,B,C,D be sets. Prove that (A∩B)×(C∩D)=(A×C)∩(B×D)

A:

Q: %3D Let C, D be subsets of a set U. By proving two inclusions, show that (CC n D) U (Cn D) = D where…

A:

Q: (ANB) –C= (A –C)NB.

A:

Q: (a) Construct a Venn diagram that expresses the meaning of AAB. (b) Соmpare АДB to BAA. 2. UNION,…

A: Consider two sets A and B, the symmetric difference between the two sets can be given as,…

Q: Let U= {1,2,3,4,5,6,7,8,9,10,11} A= {3,5,8,11} B= {2,5,6,7,8} C= {3,4,6,7,8,10,11} D= {1,3,5,6}…

A:

Q: Exercise 3.3.15. Prove or find a counterexample to the following statement. Let A, B and C be sets.…

A: We have a statement  Let A, B and C be sets. Then (A - B) U C = (A U B U C) - (A ∩ B).

Q: Let A and B be subsets of U, n(U)=90, n(A’∩B’)=20, and n(A–B)=n(B–A)=30. Determinen(A∩B).

A: It is given that A and B be subsets of U.