need help with three conceptual calculus problems!

ok so 1.

true or false (and provide reasoning, not a full length proof) that

lim as x -> a of f(x)*g(x) can not exist

if lim x->a f(x) and lim x->a g(x) both exist

so its kind of a reasoning to show that the product limit law always works if both limits exist?

2. In the formal definition of limits: lim x->c f(x) = L, if for every E>0 there is a d>0 such that IF 0<|x-c|<d THEN |f(x)-L|<E

can you switch the inequalities after the IF and THEN, and does the definition still hold?

3. TRUE or FALSE

f(x) = 1 if x is rational

= 2 if x is irrational

the limit as X-->0 exists for f(x)

im not sure about this one cause of whether the right and left hand limits meet and if so, at 1 or 2??!?!

thanks! please do asap