Let A = {a, b, c, d} and let R = {(a, a), (a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, c), (c, d), (d, d)} be a relation on A. Proof step by step if this holds for transitivity.

Q: Let U=(1, 2, 3, 4, 5, 6, 7), A=(1, 3, 5, 7), and B=(2, 5, 7). Find the set AnB AnB= (Use ascending…

A: Note: The complement of set A is defined as a set that contains the elements present in the…

Q: Show that the set S= {(1, 2, 1), (3, 1, 5), (3, -4,7)} u de nendent where. SCV (B). is linearl

A: We need to find scalars c1, c2, and c3, not all zero, such that   c1(1, 2, 1) + c2(3, 1, 5) + c3(3,…

Q: Which of the following sets spans Rº 3 None O {(1,2,3),(0,0,0)(-2,1,0)} {(2, – 1,2),(4,1,3),(2,2,1)}…

A: vectors span R3 means that some combination of the vectors can take up all of the space in R3.

Q: Let A= {1,2,x,y,z}, and B= {1,2,3,z}. How many distinct elements are in (A*B) intersect (B*A

A: Given that A=1,2,x,y,zB=1,2,3,z To find the number of distinct elements in A×B∩B×A:

Q: -8. a. Show that if A and B are independent, then P(A|B) = P(A). b. Say we have sets A, B, and C (do…

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Q: Define relations S and R on the set A = {x, y, z, w} as follows S = {(y, x), (x, w), (w, z), (x,…

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Q: Let U be a universe and let A, B, C, D be any subsets of U. Prove or disprove the following…

A: Given U be a universe and let A, B, C, D be any subsets of U. We have to prove or disprove the…

Q: If ACB then (UNA)U(BNA)=B. TO نقطة واحدة If X = (A, A, = (-1- i,1+i), iEN }, then nA = empty set. F…

A: 1 If A⊆B. Check whether U∩A∪B∩A=B Take LHS  U∩A∪B∩A=A∪B∩A    ∵[A⊆U]=A∪A          ∵[A⊆B]=A The…

Q: sume transitivity holds, and let A, B, and C be three bundles. Then, if A is preferred to B and B is…

A: Relexivity implies A is preferred to A.  Therefore option  reflexivity implies that A is preferred…

Q: Explain each step of this proof that C(5, 5) + C(6, 5) + C(7, 5) = C(8, 6): Proof. C(5, 5) + C(6, 5)…

A: The proof of the statement is given in the explanation part.Explanation:Steps and explanations are…

Q: Let A = {AC R| A is countable} and Az = {A c R| A° is countable} which is a measurable space? (R,…

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Q: Let U(-5, -4, 3, 4, 6), V(-4, 1, 7, 1, 0). Find the inner product U.V

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Q: Let U={1,2,3,4,5,6,7,8,9,10}. Let A={1,3,6,8,10}. Let B={2,3,5,7,8}. Determine (A−B)′

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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: 2) What rule maps ABC onto A'B'C'? A. (x,y) → (x+4, y = 4) B. (x,y) → (x-3, y + 5) 4 (2-0)-²00) AY 5…

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Q: Let W = (0, 1, 3}, X = {1, 3, 5), Y = (3, 4} and Z = {(1, 2), (3, 4), (1, 3),(2, 4). Compute (X x Y)…

A: The given problem is to find the Cartesian product of given sets and verify the Cartesian product…

Q: A blite earh vastor as Vectors in S. (if not posi ble, enter IMpossiecE) a limeor Combimation f the…

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Q: Let T : Ra[r|→ RĄI] be a linear transformation have matrix 1 -1 -2 with respect to the basis B = (1…

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Q: The reflexive closure of  R={(1,1),(2,1),(1,2)}R={(1,1),(2,1),(1,2)} on the set \( A=\lbrace{1,2,3…

A: The set A={1,2,3} The reflexive closure is obtained by adding a,a to R for each a∈R since (1,1) is…

Q: Let U {1,2,..., 100}, and let A consist of 15 unknown numbers taken ran- %3D domly from U. Let B…

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Q: When is S \ T = T \ S for sets S, T? Give an example

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Q: Find an eguaton for the set of all points (a sy, z) equiditant fom point (1,0,2) and

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Q: I. Let the universal set U = {1, 2, 3, ..., 10} . Let A = {1,4, 7, 10}, B = {1, 2, 3, 4, 5}, and C =…

A: According to our guidelines we can answer only first three sub-parts and rest can be reposted.

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

A: As per the norms, we will be answering the first question. If you need an answer to others, then…

Q: Relations Given the sets over the domain {a, b, c, d}: A = { (a, a), (b, b), (d, d), (b, a) } B = {…

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Q: Let X= a, b, c, d, and classify each of the following as -algebra or not justifying all your…

A: Here X = {a, b, c, d}    Any collection à of subsets of X is a σ-algebra if it satisfies following…

Q: Let E = [-5,20), be the universal set and Y =[-2,4], and Z = (0,10]be the subsets of %3D %3D Find:…

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Q: Prove that |(a, b)| = |(c, d)| for any numbers a, b, c, d where a < b and c < d. Proof: Prove that |…

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Q: A = {1, 2, 3, 4} B = {2, 4, 6, 8} 26. Conjoining strings {(x,x) & A} 27. String concatenation {(x,…

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Q: Q. Let X = {m, n}, and = {ø, X, {m},{n}}. %3D Define the function un: -[0, 00) by 3 if n e A 0 if n¢…

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Q: Let a, b e N. Choose all correct statements. O gcd(a, b) = gcd(-a, -b) O gcd(a, b) = gcd(a², b²) O…

A: We apply property of GCD to solve the problem

Q: Let A={1,2,3,4,5} and…

A: Let A=1,2,3,4,5 and R=1,1,1,3,1,4,1,5, 2,2, 2,3, 2,4, 2,5,  3,3, 3,4, 3,5, 4,4,  5,5 (a) The…

Q: Which of the following sets spans R? O (3,0,2).(5,1,0),(0,-1,1)} O (-3,0,2),(0,0,.0)} (-3,0,2)) None…

A: To finds sets that spans R3

Q: A = {q, s, u, w, y} B = {q, s, y, z} C= (v, w, x, y, z). List the elements in the set. (Au B)'n C

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Q: Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find B U (AN C). || {

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Q: Fast

A: Let U = {q, r, s, t, u, v, w, x, y, z)A = {q, s, u, w, y}B = {q, s, y, z}C = (v, w, x, y, z)Formula…

Q: Let U= {1,2,3,4,5,6,7,8,9,10,11} A= {3,5,8,11} B= {2,5,6,7,8} C= {3,4,6,7,8,10,11} D= {1,3,5,6}…

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Q: Let U = {b, e, f, g, h, j, m, o, q) A = {b, e, h, m, q} B = {e, h, q} Apply DeMorgan's Law 2 to show…

A: Solution-A={b,e,h,m,q}B={e.h.q}U={b,e,f,g,h,j,m,o,q}We have to find (AB)