In this last lesson of boolean algebra, we learned some common identities. Identities refer to the things that are always the same. For instance, A+B and B+A are always the same, so A+B and B+A are identities, we write A+B=B+A.
Some commonly used identities in Boolean Algebra are below.
#9 above is also called Law of Tautology. We can use these identities to simplify compound boolean expressions. While applying these identities, please keep in mind:
A * or a dot both means AND, and sometimes we even omit them. i.e. AB, A*B, A&&B all mean A AND B.
A bar on top of a variable means NOT, just as ! and ~. A bar on top of a compound expression means to negate the whole expression.
See the example below. Solution I and II both simplify this boolean expression.
Simplify the following boolean expressions:
2. Use DeMorgan's Law to simplify the following: