Problem 8 (#2.2.8).Prove the idempotent laws by showing a) A∪A=A. b) A∩A=A.

| Consider the elliptic curve group based on the equation y? = x' + ax + b mod p where a = 4, b = 1, and p = 7. This curve contains the point P = (0, 1). The order of this elliptic curve group is the prime number 5, and therefore we can be sure that P is a primitive element. Another element in this group is Q = (0,6). The index of Q with respect to P is the least positive integer d such that Q = dP. What is d, the index of Q?

Use Numpy to complete the following task(s). 8. Solve Assignment 5.1 #4a. 4. Let A = [2] 21 a. Give the characteristic equation of A and verify that A satisfies the characteristic equation. Characteristic equation of (A) = |xI - A| = 0

a) State the inverse and contrapositive of the statement "W whenever he comes". b) Let A, B and C be sets. Prove that A-(A-B) = A N B. c) Find all m 2 1 such that 27 = 9 (mod m). %3D

Could you assist me with this problem? I'm having difficulty understanding it and would really appreciate your guidance. Would you mind providing a thorough, step-by-step explanation to help me comprehend it more effectively?