This question seems easy enough but I want to make sure

Q) Use the definition of a Boolean Algebra to give reasons for each step in the proof below:

Proof:

Let a be any element of B, then

first step. is like saying a and 1

second step so we get

third step is distributive, the + is similar to an 'or' in logic

fourth step similar to a set and its complement yield the empty set

fifth step is the left over which is similar to a set intersect itself