# Why is Pure Mathematics so much easier than Applied Mathematics? [closed]

I love pure mathematics, so much. However, I recently did probability and statistics and applied mathematics courses, and I'm confused with statistics. There's no proofs and logic in applied math courses. I've always wondered why $$P(A \cup B)=P(A)+P(B)- P(A \cap B)$$.

• For the last statement, you should look at the Kolmogorov probability axioms. It is a straight forward proof once they are assumed. (And you know basic set theory)