Boolean absorption

A and ( A or C ) = A

And


A or A and C = A

How do these identities work?

Using the rule


A and ( B or C ) = A and B or A and C

For the first identity, I get


A and A or A and C = A or A and C

How is the C eliminated?

Mental substitution shows that it will equal A, but can it be algebraically shown.

Equation 2, too.

Here is one way to prove the first identity:
$$
A \land (A \lor C) = (A \lor 0) \land (A \lor C) = A \lor (0 \land C) = A \lor 0 = A.
$$
The second identity has a similar proof. Alternatively, you could use duality to deduce it from the first identity.

StackExchange Computer Science Q#70886, answer score: 17