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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, and describe the distinct equivalence classes of R.
(b) Why is the relation R2 on S given by xR2y iff xy < 0 NOT an equivalence relation?
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The population of a city is observed as growing exponentially according to the function P(t) = P0 e kt , where the population doubled in the first 50 years. (a) Find k to three
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