Egoism vs. Egotism

First the definition:

Egoism is a school of philosophy that says, “Only I exist. Everything else is  the product of my imagination.”
Egotism says “I am better, more important than, everyone and everything.”

Now the test. Does this guy have it right or wrong?

If you said he has it wrong, you’d be right!

Now how about this one?

Yup! He used the correct word.