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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.
Example: Solve following. | 10 x - 3 |= 0 Solution Let's approach this one through a geometric standpoint. It is saying that the quantity in th
three consecutive odd integers such that the s f the first and second is 31 less than 3 times the third. find the inters.
3x+y=-2 6x+2y=10
3x-2(4x+9)=-58
let x,y,z be the complex number such that x+y+z=2,x^2+y^2+z^=3,x*y*z=4,then 1/(x*y+z-1)+1/(x*z+y-1)+1/(y*z+x-1) is
m?1=m?2 m?2=75 m?1=75
in a cloths shop reduces it prices by 20% how much is it on sale
The "humps" where the graph varies direction from increasing to decreasing or decreasing to increasing is frequently called turning points . If we know that the polynomial con
Lisa and Judy read mystery novels. Judy has read three fewer than five times as many as Lisa. Equation: J=5L-3 Lisa: Judy:
k^(2-) k-30
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