assume that Pr[A]=0.2Pr[A]=0.2 and Pr[B]=0.3Pr[B]=0.3.   If A⊂BA⊂B, then Pr[A∪B]= If A∩B=∅A∩B=∅, then Pr[A∪B]=  If A∩B′=∅A∩B′=∅, then Pr[A∪B]=Pr[A∪B]=

Q: (c) For the set A = {[0], [6]} ≤ Z12 determine the set U = h(A). Then for the set UC Z18 determine…

A: In group theory, sets like Z12​ and Z18​ are examples of cyclic groups under addition modulo 12 and…

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):…

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Q: (c) Let X, Y and Z be sets. Prove that (X\Y)n (X \ Z) = X \ (YUZ).

A: We prove the given statement by using set theory.

Q: Make a logic circuit of the following Boolean Function. • F(x, y) = xy + x • F(x, y, z) = xz + xy

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Q: Let u = Al 2 [R and v= find a and b such that au + bv [:] 3

A:

Q: Let G = <a, b | a2 = b4 = e, ab = b3a>.a. Express a3b2abab3 in the form bia j, where 0 ≤ i ≤ 1…

A: Given that G=a, b| a2=b4=e, ab=b3a. We have to express a3b2abab3 and b3abab3a in the form biaj where…

Q: Let  X And Y are sets. Give a direct proof for X∩Y⊆X

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Q: (а b)с + (а - с)b + (с b)a 3 ve that v belongs to B.

A:

Q: If f(x1,..,x „,0) = g(6,0) h(x,..,x„), then ê® is Select one: a. sufficient b. efficient C.…

A: Introduction :-  We have to select most correct option for the given statement. Basically it is a…

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A:

Q: Let S1= {1, 5, 10, 15, 20} and let S2 = {1, 2, 3, 4, 5}. What is: (a) S1 ∪ S2 (b) S1 ∩ S2 (c) S1 –…

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Q: Find the null space for A. 12 0 [4] -3 -4 -1 6-6 9 A = null(A) = span 100

A: The given matrix is A=120-3-4-16-69 We have to find the null space of the given matrix.

Q: Let A = {1,2,3} and let R= {(1,1), (2, 2), (3, 3), (1, 2), (2, 1), (3, 2)} C A x A. In each case,…

A:

Q: Let A = {x, y, z} and B = {w, x, y}. List the elements of ℘(A). Find ℘(A) ∩ ℘(B).

A:

Q: Let X and Y be sets with A,B ⊆ X. If f : X →Y is a function, prove that f(A∪B) =f(A)∪f(B)

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Q: Let An denote the number of lattice paths from (0,0) to (n, n) that do not pass above the diagonal y…

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Q: The div A at p(1,1,2) for A is .... Å = x²y i + 2 x z j + 4 - z² y k - 3 ( 3 зі зј о

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Q: Find P(C1)  l. Find P(V4)  m. Find P(C1 ∩∩ V4)

A: As per guidelines we are allowed to solve maximum of 3 sub parts If you need help with other…

Q: 3. Let V be the set of all ordered triple in R³, and F, the set of real numbers, where the…

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Q: Let A and B be sets. The symmetric difference of A and B, denoted A∆B, is the set A∆B = (A −B) ∪(B…

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Q: 1 Assume that Pr[A]=0.45 Pr[B]=0.65, and Pr[A∩B]=0.25  A. Pr[B Compliment ∩ A]= B. Pr[A Compliment…

A: Given, Pr[A]=0.45 Pr[B]=0.65 Pr[A∩B]=0.25

Q: - If A = {2,3} and B = {x | x ≤ Z+,x <3}, then A x B= Select one: O a. {(1,2), (1,3), (2, 2), (2,3)}…

A: Given that the setsA=2,3 and B=x | x∈Z+ , x&lt;3

Q: Let a,b be two different points in R^n one. We notice that d=(a,b)>0 (why is that so ?). Prove that…

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Q: Let fi = 1+x + x² + x³ , f2 = 1 + 2x + 3x? + 6x³, f3 = 3+2x + ? + 5x4, and g = 1+x + 2a? + tæ³. For…

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Q: 2. Let U = {a + bx + cx2 + d³ e P3 (R) | a- 6+d3D0}, and let W = {a + bx + ca? + dx³ e P3(R)| a + 2c…

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Q: 2. Let A = {a, b, c}, B = {x, y, z}, C = {r, s,t}. Let f : A → B and g : B → C be defined by: f =…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.