e) Define W: Z -Z and V: Z → Z by the rules W(a) = a² and V(a) = a mod 5 for all integers a. Find the following: (W • V)(6) (V o W)(9) i. ii. iii. Is (W • V) = (V •W) for all integers a E Z? Justify your answer.

Q: _If A = Verify that [A-!]" = [A"]¬1 ? l1 2.

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Q: Let P(x) = 2x² – 5x – 12 = (1 – 4)(2a +3). Which of the following is true? O A. For 1E[-2/7, 1),…

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Q: Which of the following is not equal to P(100, 2)? 2P100 100! 98! 9900 100P2

A: We have given, P(100,2) The number of permutations of n things taken r at a time is defined as,…

Q: Find the value of c if -226 Σ1+0 2 C = No decimal entries allowed.

A: summation (1+c)^-n from 2 to infinity converges only if |1+c|<1(1+c)^-n is a GP series. Use the…

Q: • G= *-3 ) • G = , det (G) = 10 %3D 4] Then x=12 O A) TRUE O B) FALSE

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Q: For geço (Rd), het ₁ (R²). prove loc g*h = C² (R³) and a B (9xh) = (aºg) th for any multi-index B

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Q: Let 7 be a real number. Which of the following is equal to T T -2 (ED)*+E)* r2 3 0 None of the these…

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Q: Given Q(x, y) means "x and y are real numbers such that x + 2y = 5", evaluate Vx3y Q(x, y) O True O…

A: Given that, Q(x, y) means "x and y are real numbers such that x+2y=5",

Q: finD 1) 2) g(s (x) a) p(x) x?-2x+2 b.) g4)==3x t. %3D cl.) s(x) = x-1 4) Cx))

A: Given that px=x2−2x+2, qx=3x+1, rx=x and sx=x−1. 1 We have to find the prx. prx=pxUse…

Q: (c) Prove that r| +11 36 T-1 2 +36 for all real I.

A: We have to prove that the following inequality holds: x-11x2+36≤x+1136 for all real x. We will use…

Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

Q: Let A = B = C= {x|x is a real number). Let f : A → B and g : B → C be defined as follows: f(a) = 6a…

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Q: Let a (1) b=(1 1 1), A= Determine each of the following: A (a) a (b) A b (c) 12 ⓇA (d) A 12 (e) AⓇA…

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Q: iii. P(AN B) = P(A) N P(B). iv. P(A) UP(B) C P(AUB)

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Q: 19 (e) a = 1575, b = -231 (a) 3710

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Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

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Q: If P(A) = P(B) = P(AB), show that P(AB + AB) = 0 [AB = An B]. %3D

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Q: (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b…

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Q: O d. Evaluate 3 dz (2+1)V교+2z -2 oa vSarsec (플) +c + C b. 3 arsec (1) + C C. 3 arsec (팔) +C V3 arsec…

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Q: C Compute the following expressions.

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 1. (a) 2 Let = (1, 0, -2) and = (-4, 2, 3). Find a real number x such that (ট' –æè) ⊥ à. (b)-1 (c) 3…

A: Let .To find a real number  such that .

Q: 12. Determine whether the following is true: (a) ≥3, EZ, 31(2²" - 1); n (n + 1)(2n +1) (b) 12+22+ 32…

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Q: (p v q) → r = O (p v r)^(¬q v r) O (-p v r)v(q v r) O (-p v r)v(¬q v r) O (-p v r)^(¬q v r)

A: We will find out the required value.

Q: Let = [1, -1, 1], [-2, -1, 3] and = [-1, 2, 2]. Find (u ×7)•w: O-14 07 O 10 Does not exist

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Q: Find z-transform for 8 © x(n) = 5ucn) - 2 (055 un) = 5 e(n) - 2 (0-5) u(n)

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Q: C Compute the following expressions (d) Im a+bj a+cj Im [+

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Q: O F = (W+Y+Z).(W+X+Z).(X+Y+Z).

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Q: For integers x and y, prove that x+y+xy + 3 is odd if and only if x and y are both even.

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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: For an integer t, prove that gcd(2t + 1, 9t + 4) = 1.

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Q: The dual of the following Boolean expression is (0 +1)(1+ yz) + 7 O (1.7) + (0.y + 2). z O (1.7) +…

A: We have to find the dual of 0+x1+yz+x

Q: Drample(2): Determine an even and odd permutations of P- (H W)

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Q: Let A = {x e Z: 10|x} and let B={xeZ:15|x}. %3D Then * O Bc A O A=B O None of these O ACB

A: Suppose A and B are two sets . Note the following result : If x∈B for all x∈A then A⊆B . If A⊆B and…

Q: Q2/ prove [A] [A] = [I] if [2 4 -5 [A]= 2 7 1 3 4

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Q: IF| = r r) = -i = 5xi + 2yj – 2zk so be it where div() , grad(f find all of

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Q: 1- Prove that (a) |A× B|² = |A|2|B|? – (A · B)² (b) (Ax B)(C × D) = (A· C)(B· D) – (A · D)(B · C)…

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Q: Suppose (x1,x2) + (Y1,Y2) is defined to be (x1 + Y2 ,x2 + Y1). With the usual multiplication cx = (…

A: It is given that the addition is defined as x1, x2+y1, y2=x1+y2, x2+y1 and the multiplication is…