Question

Boolean Identity (A→ + B→).(A +B) is equal to

Answer 1

To solve the given Boolean expression, we need to simplify it using Boolean algebra identities. Given:
\([ (A' + B') \cdot (A + B) ] \)
Where: A' is the complement (NOT) of A 
B'  is the complement (NOT) of B
 To simplify, distribute the terms using the distributive property: 
\([ = A'A + A'B + B'A + B'B ] \)
Let's simplify each term: 
1. \(( A'A )\) will always be 0 because it is the AND operation between a variable and its complement. 
2.  B'B  will also always be 0 for the same reason. So the above expression reduces to: \([ A'B + B'A ] \)
This is the Boolean expression for the Exclusive OR (XOR) operation: \([ A \oplus B ] \)
So, the simplified Boolean expression for \(( (A' + B') \cdot (A + B) ) is: [ A \oplus B ]\)