"not p and p" is a contradiction. What does this tell you?

Edit: Maybe it will make more intuitive sense if you put statements in.

"It is true that I'm not happy and that: I'm happy or rich (or both)." Do you see why this in all cases implies that "I'm rich"?

Edit 2: Sorry didn't notice the "without truth tables" part.

This might not be quite right, but here's my attempt

not p and (p or q) <-> (not p and p) or (not p and q) <-> not p and q

so we have

not p

q

--------

therefore q

which is a tautology because the conclusion is the same as one of the premises.