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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 equivalenc
Let G be a group acting on a set X. The action is called faithful if for any g ≠ 1 ∈ G there exists an x ∈ X such that gx ≠ x. That is, only the identity fi xes everything. Prov
A passenger jet took 3 hours to fly 1800 km in the direction of the jetstream. The return trip against the jetstream took four hours. What was the jet's speed in still air and the
f all the permutations of the letters of the word chalk are written in a dictionary the rank of this word will be?
Find out all the critical points for the function. Solution Following is the derivative for this function. Now, this looks unpleasant, though along with a little fa
When the son will be as old as the father today their ages will add up to 126 years. When the father was old as the son is today, their ages add upto 38 years. Find their present
Find out the area of the region bounded by y = 2 x 2 + 10 and y = 4 x + 16 . Solution In this case the intersection points (that we'll required eventually) are not going t
Suppose we are required to find the difference between 3abc and 7abc. We look at two scenarios. The value we would obtain by subtracting a larger quantity from th
how to answer this: 3x2-18x-60
3x2+5x-2
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