BASIC LAWS AND COMMON IDENTITIES OF BOOLEAN ALGEBRA
1.
IDENTITY:
A=A
A=A
2.
COMMUTATIVE:
AB=BA
A+B=B+A
3.
ASSOCIATIVE:
A (BC) =A B C
A +( B + C) = A + B + C
4.
IDEMPOTENT:
AA=A
A+A=A
5.
DOUBLE
A=A
NEGATIVE
6.
COMPLEMENTARY:
AA=0
A+A=1
A 1=A
A 0=
7.
INTERSECTION:
0
8.
UNION:
A+1=1
A+O=A
9.
DE MORGAN'S
AB=A+B
A+B=AB
THEOREM
10. DISTRIBUTIVE:
A (B + C ) = A B + A C
A + (B C) = (A + B)(A + C)
11. ABSORPTION:
A (A + B) = A
A + (A B ) = A
12. COMMON
A (A + B) = A B
A + AB
=A
+B
IDENTITIES:
A+AB=A+B
A+AB=A+B
13. DEFINITIONS:
0=1
1=0
MINTERM:
Boolean product of a number of variables (no OR, all
variables included).
MINTERM-TYPE:
A minterm with one or more variables missing.
MINTERM FORM:
Composed entirely of minterms and minterm-type terms
connected with ORs, but no parentheses or vincula
extended over more than one variable or more than one
vinculum over a variable.
IT0345
1-70
Previous Page
