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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?
Define an ordered rooted tree. Cite any two applications of the tree structure, also illustrate using an example each the purpose of the usage. Ans: A tree is a graph like t
Draw the graph of y=x^2-4x from x=-1 to x=5.use the scale of 2cm on the x axis and 1cm on the y axis.Estimate the gradient at point:x=4, x=2 and x=0
1.A manufacturing facility consists of five departments, 1, 2, 3, 4 and 5. It produces four components having the manufacturing product routings and production volumes indicated in
Differentiate the following functions. (a) f (t ) = 4 cos -1 (t ) -10 tan -1 (t ) (b) y = √z sin -1 ( z ) Solution (a) Not much to carry out with this one other
trigonometric ratios of sum and difference of two angles
Hypothesis Testing About The Difference Between Two Proportions Hypothesis testing about the difference between two proportions is used to test the difference between the propo
This time we are going to take a look at an application of second order differential equations. It's now time take a look at mechanical vibrations. In exactly we are going to look
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Hypergeometric Distribution Consider the previous example of the batch of light bulbs. Suppose the Bernoulli experiment is repeated without replacement. That is, once a bulb is
Suppose you are in the market for a new home and are interested in a new housing community under construction in a another city. a) The sales representative informs you that the
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