For f (a, b) = (a | b) | b (a) Simplify f (a, b). (b) Find DNF for f (a, b). (c) Is f (a, b) satisfiable?
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For f (a, b) = (a | b) | b
(a) Simplify f (a, b).
(b) Find DNF for f (a, b).
(c) Is f (a, b) satisfiable?
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- Let R=ABCDEGHK and F= {ABK→C, A→DG, B→K, K→ADH, H→GE} . Is it in BCNF? Prove your answer.Assume that A is reducible to B. Show that if B is solvable in polynomial time, then A is also solvable in polynomial time.Match the following sentence to the best suitable answer: - A. B. C. D. for the linear congruence ax=1(mod m), x is the inverse of a, if__________ - A. B. C. D. What is -4 mod 9 ? - A. B. C. D. The solution exists for a congruence ax=b(mod m) such that GCD(a,m)=1 and - A. B. C. D. (107+22)mod 10 is equivalent to :_________ A. 5 B. c divides b C. GCD(a,m)=1 D. 9 mod 10
- 1. Consider an impulse response h[n] such that h[n] = 0 for n < 0 and n > M, and h[n] =−h[M − n] for 0 ≤ n ≤ M where M is an odd integer.a) Express the Fourier transform of h[n] in the formH(ejω) = ejf(ω)A(ω) ,where f(ω) and A(ω) are real-valued functions of ω. Determine f(ω) and A(ω).b) Provide an example of such an impulse response h[n] for M = 7 and find the corresponding f(ω) and A(ω).Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = x ^2. The composition of fog (-2) is --Let A={+,x,a,b}. Show that (a*V ba)+ b is regular over A.
- Suppose that C is a linear code with Hamming weight 3 and that C'is one with Hamming weight 4. What can C' do that C can’t?Prove or disprove that for any x ∈ N, x(x+1)/2 ∈ N (where N = {0, 1, 2, 3, ….}Suppose that the equation ax b .mod n/ is solvable (that is, d j b, whered D gcd.a; n/) and that x0 is any solution to this equation. Then, this equation has exactly d distinct solutions, modulo n, given by xi D x0 C i.n=d / fori D 0; 1; : : : ; d 1
- implement program to Finding the Longest Common Substringproblem that lends itself to a dynamic programming solution is finding the longest common substring in two strings. For example, in the words “raven” and “havoc”, the longest common substring is “av”.Compute the gradient with respect to all parameters of f(w0 + w1a1 + w2a2) when w0 = 3, w1 = −2, a1 = 2, w2 = −1, a2 = 4, and β = 0.25 using backpropagation(3a) Compute the stability function S of the Rosenbrock method (108), that is, compute the (rational) function S(z), such that y1 = S(z)y0, z ∶= hλ, when we apply the method to perform one step of size h, starting from y0, of the linear scalar model ODE y˙ = λy, λ ∈ C