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1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y).
(a) Prove that R is an equivalence relation on Z.
(b) If for every x ? Z, the equivalence class of x, [x], contains exactly one element, what can be said about the function f?
10+2=
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Smith keeps track of poor work. Often on afternoon it is 5%. If he checks 300 of 7500 instruments what is probability he will find less than 20 substandard?
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