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 selfinverses 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 selfinverse 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?
