Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC) × (Bn D)

Q: verify that (AB)C = A(BC)

A: Given matrices:

Q: b) 568 mod 7

A:

Q: assume that A={6,8,4,g} and B={3,2,8,d,h,g}. (a) n(A×B)= (b) n(B×B×B)=

A: a) Given that A={6,8,4,g} and B={3,2,8,d,h,g}So, A has 4 distinct elements and B has 6 distinct…

Q: a (1, 0, 1), b = (2, 1, −1) and c = (1, -1, 4). Calculate |ax (b+c)].

A:

Q: 3 Let x = (9, −9, −4) and y = (-6, 6, -9) be in R³ and a be in R. Then ax + y = ( ,23).

A:

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

A:

Q: A = Acosx + Bsinx + 1 and B = -Asinx + Bcosx Then, what is the A, B ?

A: The detailed solution is given below  Thank you

Q: Evaluate SA(u) du if A(u) a) 6i+8k b) -6i+8k c) 61-8k (3u²-1)i + (2u-3)j + (6u²-4u)k. d)-61-8k

A:

Q: b) Let: [1 1 0] A = 0 2 3 10 1 and B = 0 2 Determine: (i) AB. (ii) A+ A".

A:

Q: Is (2,1)=(1,2)?

A: The objective is to determine whether 2,1=1,2.

Q: Provide an interpretation which is true and one that is false. (∃ x)(P(x,b))

A:

Q: TRUE or FALSE: A\B = A when A and B are disjoint

A: Given statement ,A|B=A then A and B are disjoint

Q: 49. Prove that (a – b) × (a + b) = 2(a × b).

A: The following properties of vectors are used in proving the given identity. a×a=b×b=0a×b=-(b×a)

Q: Prove: a) P(AnB) = P(A) + P(B) - P(AUB) b) P(AnB) = P(A) - P(A-B)

A: This prove can be done using Venn diagram easily. Take a sample space S in which two event are…

Q: Verify that (a) A(BC)= (AB)C and that (b) A(B+C) = AB + AC.

A:

Q: Let u = and v = Find each quantity: a) (u)(v)  b) (u)(u)  c) (v)(v)

A: Given: u =<4,-3> and v =<-2,7>

Q: actortise the expression: a^(2)+by^(2)+bxy +axy

A: Given expression: ax² + by² + bxy + axy

Q: Let ged(a, b) = d then which of the following is correct @ dla (i) dlb (i) dl(ax + by) (a) only (i)…

A: gcd(a,b) = d

Q: 4 n3 + 2 n=1 00 4n n=1 00 3n nn n=1 8. 8. 8.

A: According to our company's guidelines I can only answer first three subparts of the question, since…

Q: a+2b 2 Let W = :a,be R}. Show that -4 lies in W. 2a -1

A:

Q: Prove that |A \(BUC) = (A \ B) \ C.

A: We have to prove in explanation section please check it.Explanation:If you have any questions please…

Q: If 8 = (AB)–- (AB), then with usual notation, prove that %3D (i) [(A)- (a)] [(B)- (B)] + 2 N 8 (AB}…

A: ANSWER: For the given data,

Q: (d) Qn (0,1)

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.