QUESTION 21 Simplify the boolean equation given below?

When A = 1, the term A dominates and makes Y = 1. When A = 0, the term (A + B)' = (0 + B)' = B', and A'B = 1·B = B, so Y = B' + B + 0 = 1 (by the law of complementarity). Therefore, Y is always 1 regardless of input values.

Step-by-step Derivation:
Step 1: Apply De Morgan's Law to (A + B)': (A + B)' = A'B'

Step 2: Rewrite the equation:
Y = A'B' + A'B + A

Step 3: Factor out A' from the first two terms:
Y = A'(B' + B) + A

Step 4: Apply the complement law (B' + B = 1):
Y = A'(1) + A
Y = A' + A

Step 5: Apply the law of complementarity (A' + A = 1):
Y = 1

Verification by truth table:

All outputs are 1, confirming Y = 1.