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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?
Multiply following. Assume that x is positive. (3√x-√y)(2√x-5√y) Solution (3√x-√y)(2√x-5√y) =6√x 2 -15√x√y-2√x√y+5√y
What is a set? Explain various methods to represent a set in set theory. Define the following with the help of suitable examples. (i) Singleton Set
Raul's bedroom is 4 yards long. How many inches long is the bedroom? There are 36 inches within a yard; 4 × 36 = 144 inches. There are 144 inches in 4 yards.
Seth has a pet goldfish. When he got his goldfish , it was only 5 centimeters long . Now it has grown to be 92 millimeters long. How many millimeters has the goldfish grown since
how it is
Differentiate following functions. h (t ) = 2t 5 + t 2 - 5 / t 2 We can simplify this rational expression as follows. h (t )
what does 1000/q in the ATC equation represent economically?
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adison earned $25 mowing her neighbor''s lawn. then she loaned her friend $18, and got $50 from her grandmother for her birthday. she now has $86. how much money did adison have to
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