A and ( A or C ) = AAnd A or A and C = AHow do these identities work?Using the ruleA and ( B or C ) = A and B or A and CFor the first identity, I get A and A or A and C = A or A and CHow is the C eliminated?Mental substitution shows that it will equal A, but can it be algebraically shown.Equation 2, too.
Boolean absorption
boolean algebra
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.