Question

Prove using Boolean Algebra

A+A'.B+A.B'=A+B ( 'means bar ) ​

Answer 1

Answer:

A non-empty set B = (a, b, c …..) with two binary operations OR or JOIN denoted by +), AND or meet (denoted by ) and a unary operation complement (denoted by’) is a Boolean Algebra if the elements satisfy the following axioms:

Explanation:

B.I. commutative law,

(i)a + b = b + a

(ii) a.b = b.a

 

B II. Distributive law,

(i)a.(b + c) =a.b + a.c

(ii) a+(b.c) = (a + b).(a + c)

 

B III. Existence of identity elements,

There exist elements, 0, such that

a + 0 = a

a.1 =a

 

B IV. Existence of complements,

a + a’ = 1

a.a’ = 1

a.a’ = 0