Asked by JasonJones 3 years ago

Question 1

G = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176}

(G, x187)

Is a group

(H, x17)

Is a group, where H = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}. Which of the following options is true?

Question 2

G = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176}

(G, x187)

is a group. What is the inverse of 121 in G?

Question 3

G = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176}

(G, x187)

is a group. What is the identity in this group?

Question 4

G = {x, y, a, b, c, d}

(G, *) is a group under a certain binary operation *.

If x*y=a and y*x = d, then how many self-inverses does (G, *) have?

Question 5

G = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176}

(G, x187)

is a group. How many self-inverse elements are there in this group?

Question 6

Use Mathcad to evaluate the following integral to 3 decimal places

Question 7

How many solutions does the following equation have in Z_{24}

X^{2}+7x+12=0

Question 8

Give an example of a prime number p such that 43p+9 is a square number.

Question 9

Suppose p, q and r are statements. How many Ts are there in the last column to be filled in for the truth table for the following compound statement?

(p?(q?~r))?(p?q)

Question 10

Suppose n denotes a positive integer. Consider the statement S given by

S; The number n^{2}+n+17 is a prime number.

Statement S is false for many values of n, including 17 and 34.

What is the least value of n for which the statement S is false?

Answered by maddy 3 years ago

**Excerpt from file: **1. G is Abelian and G is isomorphic to H x187 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 11 121 55 176 110 44 165 99 33 154 88 22 143 77 11 132 66 22 55 110 165 33 88 143 11 66 121 176 44 99 154 22 77 132 33 176 165 154 143 132 121 110 99 88 77 66 55 44 33 ...

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`*italics*`

or `**bold**`

, to write a math equation use, for example, `$x^2+2x+1=0$`

or `$$\beta^2-1=0$$`

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Asked: 3 years ago