Let Π1, Π2, and Π3 be the problems. Prove that if Π1 ≤p Π2 and Π2 ≤p Π3, then Π1 ≤p Π3.
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Let Π1, Π2, and Π3 be the problems. Prove that if Π1 ≤p Π2 and Π2 ≤p Π3, then Π1 ≤p Π3.
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- Let E : y2 = x3 + 3x + 4 be an elliptic curve over F37. 1, Find all the elements of the elliptice curve group 2, Find the order of the 3, Find a primitive element of this group and call it G. 4, Compute [30]G = G ⊕ G ⊕ · · ⊕ G (addition of 30 many G’s)(a) Let Γ ⊂ S(P). Show that Γ |= ⊥ if and only if Γ is not satisfiable. (b) Let ∆ be a set of formulas and φ a formula in S(P). Show that if ∆,φ |= ⊥, then ∆ |= ¬φ.Find all solutions of the following congruence(s). Show all work. 2x ≡ 5 mod 89
- 1. Give solution, graph and if the point ( 3, y) is equidistant from ( 4, -2 ) and ( -1, 4)Solve each of the following congruences. (Give the complete list of solutions) (a) 2x^3 + 3x^2 + x + 1 ≡ 0 ( mod 5)Simplify the given POS function (a) k-mapping and (b) tabular method. Show your complete solution. F(A,B,C,D,E)=(0,2,4,5, 7, 8, 10, 12, 16, 18, 20, 23, 24, 25, 26, 27, 28) a. K-mapping b. Tabular method
- Find all solutions of the following congruence(s). Show all work. 2x ≡ 5 mod 7 2x ≡ 5 mod 89Given a 3-CNF formula and number k find if there exists a satisfying assignment such that at least kvariables are FALSE. Is this problem NP-complete or not? Why?Determine the value(s) of x so that the matrix below is the augmented matrixof an inconsistent linear system. x 1 5 5 -3 2