Problem 1: (a) Compute 13-1 (mod 23) by enumerating multiples. Show your work. (b) Compute 13-1 (mod 23) using Fermat's Little Theorem. Show your work. (c) Compute 11-11 (mod 19) using Fermat's Little Theorem. Show your work. (d) Use Fermat's Little Theorem to compute 71209643 (mod 11). Show your work. (e) Find an integer x, 0≤x≤ 40, that satisfies 31x + 42 = 4 (mod 41). Show your work. You should not use brute force approach. (f) Calculate 138-1 (mod 2784) using any method of your choice. Show your work. (g) How many integers have inverses modulo 144? Justify.

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: What is the relative risk for the association between men and women vs COVID-19 infection? What do…

A: Data is given for Men and women, vs Covid infection ( Covid positive and Covid negative We have to…

Q: Submit through Canvas as indicated. T u = (2,-5) and v= −3i+7j

A:

Q: Determine whether (p→q)→(q→r) is equivalent to q→r. Justifyyour claim.

A: we have to check whether  (p→q)→(q→r) is equivalent to q→r

Q: 7. f(2) = -3, g(2) = 2, f2) = 4, g(2) = -5 a) If h = 0, use the values above to find h) 9(x)

A: 7. f2=-3, g2=2, f'2=4, g'2=-5

Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

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

A:

Q: Prove by contradiction: “V3 is iirational." « 3

A: In this, we need to prove that 33 is a irrational number. So, we need to assume that 33 is rational…

Q: Verify that det(AB) = det(A) det(B) for the following:

A: Given: The given matrices are A=1-23-231010 and B=1023-25213. First, find the determinant of A and…

Q: (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}.…

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Q: b) Compute Sc C 2z²+z+₁ dz, where Z² +4 iii) C = {z: \z+i)=2

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Q: evaluate using the appropriate method or combination of methods.

A:

Q: t3 dt 6) f Vt2 + a?

A: Given Data The integral is     Let,

Q: VXVYP(x,y) is equivalent to VyVxP(x,y). O True O False

A: ∀x ∀y Px, y is equivalent to ∀y ∀x Px, y.

Q: Assume that (U)=110, n(B′)=55, n(A∩B′)=25, and n(A∩B)=27. Find n(A∪B)

A: For any two events A and B, it is known that n(A or B) = n(A)  + n(B) – n(A ∩ B).