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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 Find out all the zeroes of P ( x ) = x 4 - 7 x 3 + 17 x 2 -17 x + 6 . Solution We found the list of all possible rational zeroes in the earlier example. Follo
please help me understand polynomials- i get the small problems but i dont understand larger ones
-200t^2+3600t-6400 if the goal was to raise 8500 what would be the price of each ticket?
15+1/2x=0.60(20+x)
Subject identification numbers in a certain scientific research project consist of three digits followed by three letters and then three more digits. Assume repetitions are not all
As a last topic in this section we have to briefly talk about how to take a parabola in the general form & convert it into the following form
2.3*10^3,3.7*10^2,6.5*10^3
Five (5) years ago, you bought a house for $171,000, with a down payment of $30,000, which meant you took out a loan for $141,000. Your interest rate was 5.75% fixed. You would li
the kinetic energy of an object varies directly as the square of its velocity. A certain object traveling at 80 feet per second has a kinetic enrgy of 240 foot-pounds. what would b
if m
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