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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?
By pigeonhole principle, show that if any five numbers from 1 to 8 are chosen, then two of them will add upto 9. Answer: Let make four groups of two numbers from 1 to 8 like
problem set d, #7
Town x and town y were 270km apart. a car started from town x towards town y at a uniform speed of 60km/hr, while a motorcycle started from town y to town x at a uniform speed of 9
Explain Analytical Models in Operations Research with Application
1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0. (a) Prove that R is an equivalence relation on S, an
defination of uper boundarie .
EXPLAIN HOW MARKOV PROCESS IS APPLIED IN BRAND SWITCHING?
Compute the linear convolution of the discrete-time signal x(n) ={3, 2, 2,1} and the impulse response function of a filter h(n) = {2, 1, 3} using the DFT and the IDFT.
prove:
compare: 643,251: 633,512: 633,893. The answer is 633,512.
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