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 $( (A' + B') \cdot (A + B) ) is: [ A \oplus B ]$