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Question 1:
(a) Describe a binary operation on a set S.
(b) Give the definition of a group.
(c) State whether the following statements are TRUE or FALSE. Justify your answer.
(i) The set of natural numbers is closed with respect to multiplication.
(ii) The set of integers is closed with respect to division.
(iii) The set of rational numbers contains the additive inverse for each of its members.
Question 2: Euclidean Algorithm
(a) Explain how the Euclidean algorithm is used to calculate the greatest common divisor of two integers a and b.
(b) Under which condition does the equation ax + by = d, where a,b,c ,a,b ≠ 0, has solution in
(c) Find x, y such that 2431x + 1324y = 11.
(9x-3)(x+6)
y+7 3y-2 --- = 1 + ---- 3 5
the perimeter of a triangle is 76 centimeters. the second side is twice as long as the first side. the third side is four centimeters shorter then the second side. how long is each
if the roots of a quadratic equation are (-2+sqrt 6) and (-2-sqrt 6), what is the equation in ax^2+bx+c=0 form?
There are also two lines on each of the graph. These lines are called asymptotes and as the graphs illustrates as we make x large (in both the +ve and -ve sense) the graph of the h
exammples
y = 5x, solve for x
5/t2 + 4/t+1
How do you graph this: (3x + 7, 2x -8); x = -3
y=-x-2 y=-5x+2
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