Here is the $$addition$$ table for the Boolean Algebra system

$0+0=00+1=11+0=11+1=1$One of these results differ from our usual addition rules, and since $1$ and $0$ are the only possible inputs these four statements comprise the entire set of rules for Boolean addition

a$)$ Suppose a student $($such as yourself$)$ saw this for the very first time and was puzzled by the above outcomes; how would you explain the rules for adding in the Boolean Algebra system to the student?

b$)$ Considering the outcomes, which logic term could be used to describe the operation of $$addition$?$