Let U be a universe and let A, B, C, D be any subsets of U. Prove or disprove the following statements: (a) (A x B) n (C x D) = (An C) x (Bn D) (b) (A x B) U (C x D) = (AUC) x (BUD)

Q: Let U = {1,2,3,4,5), A = {1,3,5}, B = {1,3,4), and C = {2,3,5). (a) Find A U (BUC). (b) Find (AUB)…

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: Show that If (A ∩ B = ø) then P (A ∪ B) = P (A) + P (B)

A: Given that A ∩ B = ø This means P(A ∩ B ) = 0

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

A:

Q: a. Vitali Theorem

A: a) Here, the Vitali Theorem has to be defined and it is also defined as a fundamental result in…

Q: 5 = { [²] [3²] [37] 3 a) Determine if S = is an orthogonal set. b) True or False. If A = ²24 then A…

A:

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

A:

Q: Let f AB, prove the following: (a) if S, T are subsets of A, then f(SNT) ≤ f(S) nf(T); (b) if U, V…

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: 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: Q.No.3 a) Prove that if A and B are sets, then (An B)U (ANB') = A

A:

Q: a) Let A = {4, 7, 8} and B = {−1, 5}, Find and compare sup(A+B) , inf(A+B), sup(A)+sup(B),sup A -…

A: See the attachment

Q: Prove that ∀a, b, k ∈ Z that ((4|k) ∧ (k = ab)) ⇒ (2|a ∨ 2|b)

A:

Q: tor all l sets A, Bad C やok that A xCB-c) = (AX1B J- CAxc). %3D

A: Given below the detailed solution

Q: [Falkner Section 11 Exercise 15(b) – modified] Let S and T be sets. Prove that S and T are disjoint…

A:

Q: According to Bayes' Theorem, letting p = P(A), q = P(B), r = P(A|B), we can express P(B|A) as...…

A: Given that P(A) = p P(B) = q P(A | B) = r

Q: 1. If ü= (2,-3), v=(1, -5), and w=(6, 2), determine the following: a) |ü +v| b) 3 ỹ -ū +w

A: a) u→+v→=(2,-3)+(1,-5)=2+1,-3-5=3,-8=32+(-8)2=9+64=73|u→+v→|=73

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: Let A, B, C subset U. Suppose that n(U)= 90, n(A)= 40, n(B)= 55, and n(C)= 20. Which of the…

A: Answer

Q: Prove that |A U B| + |A n B| = |A| + |B|

A: Let A and B are two sets. A = number of elements in the set A. B = number of elements in the set B.…

Q: (b) If WCU, prove that (Recall that U+W = (c) If U + W = U, prove that WCU. U + W = U. = {u+w|u€ U₁w…

A:

Q: I need help for number 7. Thanks!

A: (a)Let

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

A:

Q: Suppose A, B, C are sets. Prove that (AUB) – C = (A − C) U (B − C)

A: A∪B-C=A-C∪B-C

Q: . Consider the statement: Let A, B ∈ Z. If 6|A and 10|B, then 4|(A2 + B2). (a) Prove the statement.…

A: 5. Consider the statement: Let A, B ∈ Z. If 6|A and 10|B, then 4|(A^2 + B^2). (a) Prove the…

Q: 2. Find a set A such that A = {2, JA]}.

A:

Q: Q#6. Given any sets A and B define the symmetric difference of A and B (ΑΘΒ) -(Α-Β ) υ (B - Α) prove…

A:

Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B) n (AUC)

A:

Q: (m) W ) Given A, Be {sets}, V AC B, A – B= A.

A: Given: A,B∈sets and A⊂B since A⊂B⇒A-B=ϕ we have to prove A-B=A So, these will happen when A=ϕ So,…

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

A:

Q: Prove or disprove the following statement: "For all real numbers x, y, [xy] = [x][y]." (3 marks)

A: Introduction: Two important functions are frequently used in mathematics and computer programming.…