n ∈ Z, d ∈ N} and define (a, b) ≡ (c, d) to mean ad = bc 1. For any (n,d) we have (n,d) ≡ (n,d) 2. If (a,b) ≡ (c,d) then (c,d) ≡ (a,b) 3. If (a,b) ≡ (c,

Q: 3. It has to: i = (2, –3,4); i = (-5,1,0); w = (4,2,1), perform the following operations: u+v; u-w,…

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Q: Let A=(1, 0), B=(0, 1), C=(1, 1), and D=(r, 1). Verify that R(A, B, C, D) = r.

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Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x>5}. Find d. A-D e. A x B f. BxB g.…

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Q: Ex. Show that [b, c) ~ [a, o), where a, b, c ER and b< c. [H7-9]

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Q: Let U=​{1,​2, 3,​ ...,2400​}. Let S be the subset of the numbers in U that are multiples of 3​, and…

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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: 1-Evaluate Logs V5

A: We will use the properties of logarithms listed with each step in the below page

Q: R={(4,1) (2,2),(3,1),(3,3), (1,3)},A={1,2,3} then [1]= %3D .a {1,3} .b {2} .C {1,2,3}

A: Equivalence class

Q: If u = (3,0), v = (1,2), and w = (1, –1), find a and b such that u= av + bw b = (enter numerical…

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Q: a) PV (QAR) b) P^(-QVR) c) P⇒ (-QAR) d) P⇒ (QV¬R)

A: We are given that            P = Q = R = True (a) ¬P = False       Q ∧ R = True ∧ True = True…

Q: If w(f.9) = , then w(s.S+9) = (A) (B) - (C) 22 (D) -22 (E) None

A: Ans:- If w(f,g)=x2, then we have to find the value of w(f,f+g).

Q: Q3// Let x be a r.v having p.m.f X -2 -1 5 P(X) 20 3C 20 C 4C 1) Find the value of C? 2) Find C. d.…

A: The pmf is given as X -2 -1 0 2 3 5 P(X) C 2C 3C 2C C 4C 1. It is known fact that,  ∑ P(X)…

Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

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Q: Show that if AB = I, then det(A) 0 and det(B) # 0.

A: Here given as AB=In find determinant both sides detAB=detIndetAB=1

Q: Hiw.sLetAzi+j-2K,b=-i-k and c=zi+uj-zk,finds t Ax(B+C)- 3 CA-B)xC s-(AXB)ec 2- A (2B-c) 4-2Ax 3B 6-…

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Q: Suppose E = {a, b, c, d, e, f, g, h, i, j}, %3D A= {a, b, c, d, e, f, g}, B= {b, d, f, i, j}, C =…

A: Given sets are

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: 5. Let A 3D, В %3 and C %3 Find a) (A · B)C b) А : (2С) c) ||B||2

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Q: = (-10,6, –4) be in R and a be in R. Then , 36 , Let x ат — ).

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Q: If P(n-1,3):P(n,4) = 1:9,Findn.

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Q: Let A = ff, I, y }, B = {r, a, t}. Find A x B and B X A. AxB= qafhbuifsfvggbh

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Q: Show that S = {x* + 1, xª + x, xª + a², xª + æ*, xª} spans PA.

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Q: = Suppose (3, −1, −2), = (-1, 1, −4) and w = . 9. 9. v.w= 9. v. v= ū⋅ (v+w)= . 9. (5, 1, 1). Then:

A: For any query with the solution, please ask in the comment box.

Q: If n(A) = 46, n(B) = 19, and n(AN B) 19, and n(An B) = 4, find n(A U B).

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Q: 10.

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Q: Find N2 A 21 N 2 p(v) B, ) = N`, p (ν) Β..) A 31 Haitha.

A: We have to separate N2 from the equation

Q: = x° + y*, ¤ = + u, and y = v – u². Find Your answer should be in terms of r, y, u, and v. dv

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Q: A = 2 1 2 0 1 -H B = W = w-B Find the following: a- A², AB, det(A) b- If AW=B, find (W) using…

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Q: Y D Prox

A: Product of two sets

Q: Let u = (2, 4) and v = (1, 12) and w=(−6, −4). Find: 12. (v.w)-(v.u) 11. 3(u-w)u 13. 2-u 14.…

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

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?

Q: Let a-2-3j.kb-41-) and c-1-31-2k. If d is such that da-9. db-7 and dc-6, then d is equal to 01-31-2…

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Q: Q9. Let keep A = (a, b, c, 1, 2, 3). Let's Insert the appropriate symbol e or ¢ in the blank space.…

A: Concept: The letter Epsilon '∈' is used for the words 'belongs to', 'is an element of', etc.…

Q: Suppose a > 0, (a, 42) = 6 and [a, 42] = 420. Find а.

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Q: 9. Given u =(2,-2), v = (5,8), and w = (-4, 3), find each of the following. (a) u v (b) (u - v)w (c)…

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Q: Let S = {Ø, 14, 1, a, 12, 17}. Then Ø C S. Select one: O True O False Let Sj = {a,b, {5}} and S2 =…

A: (1) S=ϕ,14,1,a,12,17 As ϕ is an element of S so ϕ⊆S is true. (2)  S1=a,b,5S2=b,5,c here the set 5…