Capitalization of school subjects What is the rule determinating whether or not we need to capitalize them?  Sometimes I see "Math" ; "Physics" in the middle of a sentence, and sometimes lower case is used.
Capitalize fields of study? Do I say "I study computer science," or "I study Computer Science"? Similarly, "I really liked that computer science course," vs. "I really liked that Computer Science course."
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$ $A$ and $B$ are any sets, prove that $A \smallsetminus (A \smallsetminus B) = A \cap B.$ This formula makes sense when represented on a Venn diagram, but I am having trouble with proving it mathematically.  I have tried letting $x$ be an element of $A$ and continue from there, but it doesn't seem to work out as a valid proof anyways.   Could anyone please point me in the right direction?  Many thanks.