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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.
A mountain has an elevation of 19,389 feet in 1918, the glacier on this peak covered 4 acres. By 2003 this glacier had melted to 1 acre. What was the yearlyrate of change and what
Sketch the graph parabolas. f (x ) = 2 ( x + 3) 2 - 8 Solution In all of these we will just go through the procedure given above to determine the required points and t
Suppose an economy has four sectors, Agriculture (A), Energy (E), Manufacturing (M), and Transportation (T). Sector A sells 10% of its output to E and 25% to M and retains the rest
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can you help answer this question please; four algebra formulas for Amadeus traveled 760 miles in twice the time it took his nemesis Salieri to travel 220 miles. if Amadeus"s rate
write the expression in exponential form 6^sqrt9^3
#addition of vectors is associative
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