Do the following problems using the formal proof techniques we've been discussing in class. Make sure:

you begin by stating clearly what you are trying to prove

you write the word "Proof"

everything after that is a proposition

each proposition is true (because it follows from prior steps and laws of logic; because it is a hypothesis; or because it is an assumption);

each proposition has a number to its left

each proposition has a justification (reason why it is true) to its right

your final proposition is the proposition you are trying to prove

you end with the words "QED"

Question:

Prove (for all integers a, x and y) that if a|x and a|y then a|(5*x-3*y).