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Find the generating function for the number of r-combinations of {3.a, 5.b, 2.c}
Ans: Terms sequence is given as r-combinations of {3.a, 5.b, 2.c}. This can be written or illustrated as rC3.a, rC5.b, rC2.c. Now generating function for this finite sequence is given by
f(x) = rC3.a + rC5.bx + rC2.cx2
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Let R be the relation on S = {1, 2, 3, 4, 5} defined by R = {(1,3); (1, 1); (3, 1); (1, 2); (3, 3); (4, 4)}. (b) Write down the matrix of R. (c) Draw the digraph of R.
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