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: 6. Evaluate f z z* –8 dz. A) (x² - 8) +C B) a O b O d

A:

Q: If A × B ={(p, q),(p, r), (m, q), (m, r)},     find A and B.

A: A will be the set of the first ordinates  And B is the set of the second ordinates

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

A:

Q: Suppose Duf(xo, Yo) exists. Show that Duf(xo, yo) = - Duf(xo, yo).

A:

Q: 3. Let, a, = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2 + nº+ 1, express a, in terms of n.

A:

Q: Q. One of the following statements is wrong: a.-1,0 = 1.100/ 6.(2,3=| 2.5) C. (1. 2) = R d.(2,3) =…

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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: 1-Evaluate Logs V5

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

Q: 10. Find a and ẞ such that c = αa + ẞb, where a = (-3,0,2), b = (0,-1,2), and c = (-6,5,-10).

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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: 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.

A:

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

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Q: iken that I+2=1 xpressyin terms of xand z.

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

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

A:

Q: 10.

A:

Q: If a = (2, 0, 2), b =(4, 2,-2), and c = ax (bx c) = (a x b) x c = = (0, 2, 5), show that a x (bx c)…

A: The answer is in step2.

Q: 3. Consider A={m,a,t,h}; C={x:x=3n,1sns4,neN}; B={s,t,e,m} ; D={x:x=2n,15n S6,nEN} What is ANB?

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Q: リ ー上 5, Use the inverse imatirice s tofind and (24) 22 3 ミ 3. 3. 3 -2

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Q: 13. Find B x A, if A = {0,1,2} and B = {a, b}

A: B×A={ (x,y) : x€B and y€A}

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…

A:

Q: Y D Prox

A: Product of two sets

Q: Prove that A-B=An(-B) = (-B) – (-A) = −[(-A) U B]. Also, give three expressions for An B and AU B,…

A: Difference of sets: Given two sets A and B, the difference A−B is defined as the set of all elements…

Q: Let S={(0,-1,1),(0,-2,-1),(1,1,2)}.

A: S?

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: If u x = [1, -3,5], thenx =

A:

Q: If ~v = 〈 4, 1, 6〉 and ~w = 〈3, 2, 3〉, find ~v · ~w and ~v × ~w.

A: If ~v = 〈 4, 1, 6〉 and ~w = 〈3, 2, 3〉, find ~v · ~w and ~v × ~w.

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…

A:

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: 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)…

A: