Let S = { p q |p, q are prime numbers greater than 0} and E = {0, −2, 2, −4, 4, −6, 6, · · · } be the set of even integers. . Prove that |S| = |E| by constructing a bijection from S to E.

Precipitation hardening can be achieved in many light alloys by a three-step heat treatment. what is carried out and what is the purpose at each step? why is such a treatment necessary based on the nucleation and growth theory of phase transformation. compare this treatment with tempering martensite for carbon steels (similarities and differences).