/: i am at home. /: i am playing video games. translate the following statement into symbolic form. it is not the case that i am at home and am playing video games.

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

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.