For each of the following statements, determine whether or not the assertion is true and if it is, prove that it is. If it is not, prove that it is not.

a) DES operating on a general plaintext input first with key K1 and then with key K2 produces the same output as if K2 were first used and then K1.

b) Starting with a general English plaintext P and two mono-alphabetic substitution schema, M1 and M2, the outcome of M2 applied to (M1 applied to P) is the same as the outcome of M1 applied to (M2 applied to P).

c) Using two keys K1 and K2 and the Vigenere polyalphabetic method, the result of encrypting a general plaintext first with K1 and then encrypting the result with K2 is the same as first encrypting the plaintext with K2 and then the result with K1.