Boolean Algebra
A+0=A A + A’ = 1
A.1=A A. A’ = 0
1+A=1 A+B=B+A
0. A = 0 A.B=B.A
A + (B + C) = (A + B) + C
A. (B. C) = (A. B). C
A+A=A
A.A =A
A. (B + C) = A.B + A.C Distributive Law
A + B.C = (A+B). (A+C)
A.B=A+B De Morgan’s theorem
A+B=A.B
, De Morgan’s theorem
A.B=A+B
A+B=A.B
Thus, is equivalent to
Verify it using truth tables. Similarly,
is equivalent to
These can be generalized to more than two
variables: to
A. B. C = A+B+C
A+B+C= A.B.C
A+0=A A + A’ = 1
A.1=A A. A’ = 0
1+A=1 A+B=B+A
0. A = 0 A.B=B.A
A + (B + C) = (A + B) + C
A. (B. C) = (A. B). C
A+A=A
A.A =A
A. (B + C) = A.B + A.C Distributive Law
A + B.C = (A+B). (A+C)
A.B=A+B De Morgan’s theorem
A+B=A.B
, De Morgan’s theorem
A.B=A+B
A+B=A.B
Thus, is equivalent to
Verify it using truth tables. Similarly,
is equivalent to
These can be generalized to more than two
variables: to
A. B. C = A+B+C
A+B+C= A.B.C
