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a) Let V = f1, 2, :::, 7g and define R on V by xRy iff x - y is a multiple of 3. You should know by now that R is an equivalence relation on V . Suppose that this is so. Explain the partition of V induced by R.
b) Let A = {1, 2, 3, 4} and define R on P(A) -{Ø} by xRy iff x ∩y ≠Ø. Is R an equivalence relation? Describe
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Consider the finite state machine whose state transition table is : Draw the graph for it. Ans: The graph for the automata according to the transition table is drawn b
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Question: Find the quotient and remainder when f(x) = x 5 - x 4 - 4x 3 + 2x + 3 is divided by g(x) = x-2. Make sure the quotient and remainder are clearly identified.
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IF 7 AND 2 ARE TWO ROOTS OF THE EQUATION |X 3 7 2 X 2 7 6 X |=0 THEN FIND THE THIRD ROOT IS
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