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By filling out a truth table, show that r ∧(q →p)→r→(q∧p)and ¬r∨q are logically equivalent.

Show how to reduce HAMCIRCUIT to HAMPATH in polynomial time.

the logit function(given as l(x)) is the log of odds function. what could be the range of logit function in the domain x=[0,1]?

A Boolean function simplified by using k-map has in general more terms than the product of maxterms standard form ? True False

Let Ci and C2 denote two cyclic codes with the same block length n, with generator polynomials gi(X) and g2(X), and with minimum distances dı and d2, respectively. Define Cmax = C1 UC2 and Cmin = C1 nC2. 1. Is Cmax a cyclic code? Why? If yes, what is its generator polynomial and its minimum distance? 2. Is Cmin a cyclic code? Why? If yes, find its generator polynomial. What can you say about its minimum distance?

What is big-O estimate of function f(x) = log(x^2 +1) + log(x^3 +1). Be sure to specify the values of the witnesses C and k. Show your work.

List the 4 Chebyshev interpolation nodes in the interval [0, 1] Hence, use the nodes to construct an interpolating polynomial for the function: f(x) = x ln(x + e^x)

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