Consider S3 = the set of all permutations on the set [3]. You can find these 6 permutations in the notes. Determine each of the following sets. (a) {x^2: x ∈ S3} (b) {x ∈ S3 : x^2 = e} (c) C(α) = {g ∈ S3 : gα = αg}, where α = (1 3) (d) Z(S3) = {g ∈ S3 : ga = ag for all a ∈ S3}

Q: 8.) What is the distance between an airplane flying at 120 feet above sea level and a turtle…

A: We find the distance between an airplane flying at 120 feet above sea level and a turtle swimming at…

Q: 4x-xy factors to x(2x+y)(2x-y) O True O False

A:

Q: Let {(=) = In ="(z +2)*(z² + 9)] f'(x) =

A:

Q: Q.1A) Evaluate 2 (4-x*) 4 cosy dydx 4-y

A:

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: The number ofunits in Z29[x] is 28 22 30 None

A: See the detailed solution below.

Q: A local target store bought 116 pizzas at Pizza Hut for its holiday party. Each guest ate 1/6 of a…

A: Let x be the number of pizzas bought by the store and y be the number of guests target have for the…

Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: Find 1 (9) Lp(p – 1). p(p²-1)3 (10) L-1 (p2+1)2,

A:

Q: Assume that M = N,(h) + k,h+k,h2 + kgh + k,h +.Then using Richardson's extrapolation N(h) is of :…

A: The series in the Richardson's extrapolation is given by the formula . Here, t is the positive…

Q: d. y= x² + y x + cos y

A:

Q: (f) 1 x + iy + 1 I-iy

A:

Q: Simplify the given expressions using the postulates and theorems of Boolean Algebra. a. F = xy + xy'…

A:

Q: If B' is of order 2x3 and BA is order 3x4, then A is of the order T

A:

Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

A:

Q: Let H = {(1), (12)(34), (13)(24), (14)(23)}. Find the left cosets of H in A4 (see Table 5.1 on page…

A: Given H = (1), (12)(34), (13)(24), (14)(23) in A4 H =4and A4 =4!2 =12 So , Number of distinct left…

Q: lim G 5m-7 2m+4 o Show Transcribed Text without using hopital rule

A:

Q: 6. The operation is defined on ordered pairs of integers in the following way: (a, b) (c, d) = b -d…

A: Given: a,b⊗c,d=a-cb-d

Q: Sy²el+2y®dy

A: Consider the indefinite integral ∫y2 e1+2y3 dy to evaluate the above indefinite integral, use the…

Q: P(x) = . Let and let = 10. Find P(9) x!

A: We have to find p(9)

Q: Let V3 = {(a, b)|a, b E R} with the following operations: (a₁, a₂) + (b₁,b₂) = (a₁ + b₁, a₂ + b₂)…

A:

Q: Find the Polah farm of Z=(-1+)

A:

Q: dx (1)(- 2e * )

A:

Q: think there is a mistake in the last part. It says B epsilon (x) subset =B r(x). It supposed to be B…

A:

Q: & 18) Vaing showj that the idently in

A: Using the identity 1+x2n=1+xn1+xn,                . . . (1) we want to show that 2nn=∑k=0nnk2.…

Q: List all cosets of (([1]3, [2]6)) in Z3 × Ze

A:

Q: 3 4 Evaluate [, S* 2dydx

A:

Q: 1 Use convolution theorem to evaluate L-1 (s²+9)²)

A:

Q: Evaluate х3 (x* — 1)3 dx x*(x* – 1)ª + C (x* – 1)* + C 16 4x4 (x* – 1)4 (x4 – 1)4 + C 16 + C 4

A: The given integral is; Integration of x3(x4-1)3.

Q: 14 Let /= 8, x4 dx. Select all that apply x3 - 512

A:

Q: (4 ) Let A = P{1, 2, 3, 4}). Lêt f, ĝ and h be the f:A A defined by f(X) = {1, 2, 3, 4} - X. g:A N…

A: We will directly write the image of the functions using the given definition and will use the…

Q: uestion 6: Suppose f: N N has the rule f(n) = 3n²-1. Determine whether f is 1-1.

A:

Q: Prove the following statement: (Va € Z) (Vb Z) (Vc = Z) [((a | b) ^ (a | (b+c))) ⇒ (a | 3c)]

A: