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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?
the length of three pieces of ropes are 140cm,150cm and 200cm.what is the greatest possible length to measure the given pieces of a rope?
Q. Find the number of ways three letter "words" can be chosen from the alphabet if none of the letters can be repeated? Solution: There are 26 ways of choosing the first lett
In the shape of a cone a tank of water is leaking water at a constant rate of 2 ft 3 /hour . The base radius of the tank is equal to 5 ft and the height of the tank is 14 ft.
the formulas of the area of solid figures
what is the difference between North America''s part of the total population and Africa''s part
Solving Algebraic Word Problems: What are the capacities of two water storage tanks in a nuclear facility if one holds 9 gallons less than three times another, and their whole
Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for whi
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1. Let R and S be relations on a set A. For each statement, conclude whether it is true or false. In each case, provide a proof or a counterexample, whichever applies. (a) If R
you need to cut the proper to cut 2''*4*8 long studs to the proper length to make a finished wall 8" in height underneath the studs there will be a double plate made up of two piec
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