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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.
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Synthetic division table In a synthetic division table perform the multiplications in our head & drop the middle row only writing down the third row and as we will be going thr
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Multiply 2(b + 5)
The luck dragon that live in the enchanted Forest weigh 4x pounds when they are x years old. Write a function table that can be used to find the weights of 6-year old, 8-year old,
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A boy can row a boat at a constant rate of 5 mi/hr in still water, as indicated in the figure. He rows upstream for 18 minutes and then rows downstream, returning to his starting p
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