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

18.2 billion brain cells

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 Z24 X2+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 n2+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?

19.9 billion brain cells

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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

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