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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?
Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve
#The digits 1,2,3,4and 5 are arranged in random order,to form a five-digit number. Find the probability that the number is a. an odd number. b.less than 23,000
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A man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?
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A 'woman was trying to teach her three-year-old child the numbers from 1to 5 from a children's book on numbers. Each number was illustrated by the same number of trees drawn next t
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