A requirement for a cipher is that every plaintext letter corresponds to a different ciphertext letter. If a and b are not relatively prime to n, does the affine cipher meet this property? If so, prove it. Otherwise, present a counterexample. Show your work.

7. design a circuit with three inputs (x, y, and z) representing the bits in a binary number, and three outputs (a, b, and c) also representing bits in a binary number. when the input is 1, 2, or 3, the binary output should be one lesser than the input. when the input is 4, 5, or 6, the binary output should be one greater than the input. when the input is 0, the output is 0, and when the input is 7, the output is 7. show your truth table, all computations for simplification, and the final circuit.