(a) Show that for all n € Z, n ≥ 1, if A and B₁, B2, ... are any sets, then (c) n i=1 (b) Show that for all sets A and B, the sets (A x B₁) = A x are mutually disjoint. n (₁) Bi \i=1 (A\B), (B \ A) and (An B) Determine whether the following is true A \ B = BC \ AC.

Q: 7. i) How many functions are there from the set {1, 2, 3, ...,k} where k is a positive integer, to…

A:

Q: Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

A: (d) Let, x ∈ (A')'       => x ∉ A'       => x ∈ A      So, (A')' ⊆ A. . . . . . (I)…

Q: In this question and subsequently, let d₁, d2, ..., d5 denote the first five digits of your exam…

A: Given : Let d1, d2, d3, d4, d5 denote the first five digit of exam number and X denote the set…

Q: Let S be the set S={(x+y) l 2x+3y>=(greater than or equal to) 12} What would be Sc  (S complement)…

A: The given set is: S=x,y∈ℝ2 | 2x+3y ≥12 Cleary S⊂ℝ2.

Q: (b) Let {Ai e I}. Prove that 4) =UA;. |A, iel

A: We need to prove that ∩i∈IAic=∪i∈IAic  for set Ai/i∈I We will prove using the following method: To…

Q: Let A, B, and C be sets. Prove (AUB)NC= (ANC) U(BNC)

A:

Q: prove for every two sets A and B that A=(A-B)U(A n B)

A: To prove: We want to prove  for every two sets A and B that A=A-B∪A∩B

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

A:

Q: 7. (12 points) Use a proof by contradiction to prove: For all sets A, B, and C (A\C)n(B\C)n(A\B) = 0

A: Step 1: proof  let (A/C)∩(B/C)∩(A/B)=Φ this means ∃x∈(A/C)∩(B/C)∩(A/B) Step 2:⇒x∈A/C,x∈B/C,x∈A/B…

Q: Let A and B be two measurable sets prove that if ASB then BIA is measurable and m(B\A)=m(B)-m(A)

A: The given problem is related with measure theory. Given that A and B are two measurable sets.  We…

Q: A – Ö B, = Ü(A – B.). Ü(A – B;). i=1

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: 9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

A:

Q: [2.28] Which of the following sets are convex and which are not? a. {(x₁, x₂) x² + x² ≥ 3}. : b.…

A:

Q: Determine if the following statements are true or false. Here A represents any set. (a) oCA (b) A'CA…

A: Here let us consider A to be any set which consists some elements U is a universal set  A' is a…

Q: Consider the following statements about the powersets of sets A and B. Which of them are true? 1.…

A: The true statements are:2456Explanation:

Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

A:

Q: 2. Prove for any sets A, B that (An B) = A if and only if A C B.

A:

Q: (ANB) –C= (A –C)NB.

A:

Q: 3. Express each of these Boolean functions using the operators - and -. a) x+y+z b) x + y(x + 2)

A:

Q: (b) Let={A i EN} be a family of sets with A₁ CA₂ CCA10 C... Prove that nA = A₁.

A:

Q: 6. show that the set A = {P= (₁4₁2) (R³ | 1²4 + √²2+x2 is an open out.

A:

Q: 1. Let A = {1, 2} and let B = {x, y}. Write out the following sets by listing out all of their…

A: