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Let a, b, c 2 Z+.
(a) Prove that if a|b, then ac|bc for all c.
(b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
(c) Prove that gcd(a, a + b) = gcd(a, b).
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1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0. (a) Prove that R is an equivalence relation on S, an
Can you explain that it is true that a line that slopes downward from left to right has a positive slope?
I want have material of the above topic
A function is an equation for which any x which can be plugged into the equation will yield accurately one y out of the equation. There it is. i.e. the definition of functions w
prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.
What is Partially Ordered Set? Let S = {a,b,c} and A = P(S). Draw the Hasse diagram of the poset A with the partial order ⊆ (set inclusion). Ans: Let R be a relation define
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Which of the following statements do you think are true about children? Indicate with 'T' for true and for false. Give reasons for your choice. a) Most primary school children a
a triangle with side lengths in the ratio 3:4:5 is inscribed in a circle
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