(b) Consider the set A = {1, 3, 5, 7}. (i) Determine the power set for A. (ii) Give the Cartesian product for A².
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- 6. Using the root vectors, work out the weight diagram of 10.Let E : y2 = x3 + 3x + 4 be an elliptic curve over F37. (a) Find all the elements of the elliptice curve group.(b) Find the order of the group.(c) Find a primitive element of this group and call it G.(d) Compute [30]G = G ⊕ G ⊕ · · · ⊕ G (addition of 30 many G’s) kindly help with full explanation. Thank you!Prime Implicants A prime implicant is a product term obtained by combining the maximum possible number of adjacent squares in the map. If a minterm in a square is covered by only one prime implicant, that prime implicant is said to be essential. The prime implicants of a function can be obtained from the map by combining all possible maximum numbers of squares. Consider the following four-variable Boolean function: F(A, B, C, D) = (0, 2, 3, 5, 7, 8, 9, 10, 11, 13, 15) C AB A CD 00 01 11 10 00 01 D 11 10 B
- For each of these functions, determine its domain, codomain, and range. f: Z → R, f(n) = 7Determine whether each of these functions is a bijection from ℝ to ℝ. If it is, write the inverse function. f(x) = 2x3-5(a) Draw an undirected graph G1 represented by the following adjacency matrix: 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 Does G1 contain a Hamiltonian cycle? Explain (b) Determine which pairs of graphs G1 in part (a) and G2 and G3 shown below are isomorphic and which are not, and explain your answer. If you use any invariant property in your argument, explain why this property is an invariant. Tex our answer. t 2 G2 G3 5. 7 8.
- Use two different ways to prove XY + Z = (X+Z)(Y+Z). a) Purely Algebraic way b) K-map3. Given the following minterm expansion: F(a, b, c, d) = Em(0, 2, 3, 4, 8, 10, 11, 15) Draw the K-Map Find out all essential prime implicants, do it systematically. Do you need additional loops to cover all the minterms. If yes, find the additional prime implicants. Get the minimum SOP.Program the Gaussian elimination method with no partial pivoting for solving a linear system of the form Ax=b, where b is a single column vector. Your function should take in a coefficient matrix A, and a single input vector b. Your function should return the solution vector x. Your code should also return the appropriate error message. The first line of your function should look like: function x = gaussElimination (A,b)