Absorption rule in Boolean algebra I am confused regarding the absorption rule which states: A OR (A AND B) = A.

I do not completely understand how the expression simplifies to A and while i have seen proofs for this question, i still feel that i don't completely grasp it.

I will outline my working out below:

if expression = A OR (A AND B) then, according to the commutative rule we can rewrite this as (A OR A) AND B. (A OR A) simplifies to A. This means we should be left with A AND B. However, the expression simplifies to A which i don't understand. 
Why is this the case?
One way to grasp it would be with concrete examples.

So an expression like:

"is a man" OR "is a man with a sister" (i.e. A = is a man and B = has a sister)


In this expression, if you're a man, it doesn't really matter whether you have a sister or not, you are to be counted.

or perhaps closer to a program, in an answer to "which words should we select?":

"words that start with W" OR "words that start with W and end with S"


You can see that the second condition identifies at most a subset of the first and is therefore redundant (and can safely be lopped off).

In code, you would simplify an expression like:

if s.startswith("W") or (s.startswith("W") and s.endswith("S"))


to

if s.startswith("W")


This might be why it's handy to know as a computer scientist. Conditional expressions have a tendency to become complex (and therefore difficult to reason about). Being able to simplify them safely is often a good refactoring move.

Another way to grasp it would be visually, with a Venn diagram with A and B overlapping circles. In that case, A AND B would be their intersection (the overlapping part) and the expression A OR (A AND B) would mean all points inside A or inside the intersection. Since the intersection is by definition all within A, specifying the (A AND B) intersection as an alternative is redundant.