Originally Posted by

**emakarov** You are saying this in response to what? In fact, unless you study formal logic, there is no distinction between a variable and its value. When you mention a variable, you refer to its value. Thus, we one says, "Let *a* be a rational (or irrational) number", one assumes that there is a rational (irrational) number and calls it *a*.

You should prove it using the hint in post #2.

It may. For example, "If you miss the deadline for any reason, you'll get only half the credit" means "(∃reason ...) ⇒ ..." or, equivalently, "∀reason (... ⇒ ...)", but not "(∀reason ...) ⇒ ...". I interpreted the statement the way I did because of this ambiguity of "any" and because a reasonable instructor would hardly ask to prove a statement for which a much stronger statement exists that can be proved equally easily.