This is a Logic Problem. So we need to use operators to solve this problem. There are several operators in logic. Operators can be monadic or dyadic. A monadic operator operates on a single simple statement. Other operators will all be dyadic operators because they operate on two simple statements. So in this problem we have the following operators:
1. The negation operator:
Symbol: ~
Symbol name: Tilde
Parts of negation: A simple statement with a tilde preceding it
2. Conjunction:
Symbol: &
Symbol name: Ampersand
Parts of conjunction: Two simple statements joined by the conjunction symbol.
So we can name the statements as follows:
A: I am at home
B: I am playing video games
So the translations is as follows:
~(A&B) = It is not the case that I am at home and am playing video games