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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?
[2 5] . [7 8}
One integer is two more than another. The sum of the lesser integer and double the greater is 7. What is the greater integer? Let x = the greater integer and y = the lesser int
41x + 53y = 135, 53x +41y =147 Ans: 41x + 53 y = 135, 53 x + 41 y = 147 Add the two equations : Solve it, to get ... x + y = 3 -------(1) Subtract : Solve it , to
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Quotient Rule : If the two functions f(x) & g(x) are differentiable (that means the derivative exist) then the quotient is differentiable and,
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solve x+y= 7 and x-y =21
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