Problem 2. Prove or disprove that for all sets A, B, and C, we have (a) Ax (BUC) = (A x B) U (A x C) (b) Ax (BC) = (A× B) - (A× C) 3-2 (c) Ax (BUC) = Ax (BUC) 3-1

Q: Let the domain of x and y be all people, Let W(x): "X is a woman". M(y): "y is a man", and L(x.y):…

A: Given W(x): ' x is a woman' M(y):' y is a man'

Q: Compute the following: (1) C(6,4)= (2) C(7,5)=   (3) C(9,5)= (4) C(8,3)⋅C(8,5)=

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Q: If P(A) = 0.29 , P(B) = 0.32,  P(A | B) = 0.38 then P(A ∩  B) =

A: Bayes' theorem can be used to compute conditional probabilities and isexpressed as P(A|B)…

Q: A - [4 = 2 5 5 c=[-³3 C - 1 3 2 3] 0 - 2 1 B = D= 1 5 6 1 0 - 8 2 - 4 5 0 - - 3 1 2

A: Given A=4-1023-2-521, B=15-162-3104, C=51-30 and D=135-10-2 To find-  (a) 5A-3B (b) BD

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

A: The correct option is option (d) all the three.    The detailed explanation is as follows below :

Q: 1 2 5. 2 . 5 +1. Va) da Find + C

A: Given: I=∫-5·x6+1x-2x6+1·xdx We know that; The Sum rule; ∫fx±gxdx=∫fxdx±∫gxdx The Power rule;…

Q: Suppose a and b are positive integers and 2021 α 2022 2022 b 2023 If s is the minimum value of a+b,…

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Q: (2 3. Let A = G) and B = (; ). Compute and compare: %3D a. Det(A + B), det(A) + det(B). b. det(3A),3…

A: We have A=2-135 and B=1211 Part(a) Now if we have a matrix M=abcd, then, detM=abcd=ad-bc Therefore,…

Q: (e) ((SNT)US) (f) U-S (called the complement of S) Given that the set S contains n elements, show…

A: To show that a set S with n elements has 2^n subsets, you can use the concept of the power set. The…

Q: Then, there exists k1≠0, k2≠0  such that a,b=k1c,k1d   and  c,d=k2e,k2f. a,b=k1c,d=k1k2e,…

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Q: 9. Determine the value(s) of k such that (2k, 3, k + 1) x (k-1, k, 1) = (1, -2,2).

A: (2k, 3,k+1)*(k-1, k, 1)=(1,-2,2)Find the value of k.

Q: Find x, y, z and w if (::)-(; )-(.. ") 4 x + y 3 -1 2w z + w 3

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Q: 2. Factor. a) x² 18x + 81 b) x² - 2x - 15 c) x² + 2x - 24 d) x² + 6x-40 e) x²+x-30 f) x² + 3x-35 g)…

A: Please follow the next step.

Q: Suppose that P(A) = 0.1, P(B) = 0.3, and P(A|B) + P(B|A) = 0.8. Find P(A ∩ B).

A: From the information, given thatThe formula of the conditional probability, for any two events…

Q: True or false:(a) If A2 is defined then A is necessarily square.(b) If AB and BA are defined then A…

A: We know that a square matrix is a matrix which has equal number of rows and columns. n×n is called…

Q: If A = Thus, A-1 [28] then det (A) is Choose and det(A-¹) =

A: A=28-50

Q: If P (B) = 1/4, P (A ∪ B) = 1/2 and P (A|B) = 2/3, then which of the following statements is true?…

A: GivenP(B)=14P(A∪B)=12P(A|B)=23

Q: 8. For the following statements, either prove that they are true or provide a counterexample: (a)…

A: Given that, For all integers a, b and c,  a|c and b|c Definition of divisibility: If a|c then there…

Q: Suppose f : B C where B = {a, b, c}, C = {2, 8, 10}, and f is defined by f = {(a, 8), (b, 10), (c,…

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Q: xdx 3x2 + 5 ® ;(3=° + 5) +C I + C (A) B (3x2 + 5) 7 + C + (3x? + 5) + C 12 D) (32² + 5) + C E) (3x?…

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Q: Compute det (B²), where B = 1 0 2 0 2 3 1 2 - 2

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Q: If A = {1} and B = {1, 2, 3, 4, 5} , then which of the following is(are) true? Choose one answer and…

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