Substitution rule

The laws are written with single letters, but each letter can stand for any expression, as long as you replace it the same way everywhere in the law. This is the substitution rule.

For example, the complement law says X+X = 1. Let X = AB, and you get AB+AB = 1. It is true because AB is just some value, 0 or 1, and its complement is the other one.

This is what lets the basic laws do real work. To use a law on a messy expression:

1. Look for the law's shape.
2. Say what each letter stands for.
3. Apply the law, then put the expressions back.

Some shapes to watch for:

• X+XY with X = AB: AB+ABC = AB (absorption).
• X+XY with X = B: B+BC = B+C (redundant literal rule).
• (X+Y)(X+Z) with X = A: collapse to X+YZ.

The replacement must be consistent: if X stands for AB, then X stands for AB, not AB.