The equivalent Boolean expression of AB' + AB + A'B is :

Option : 4

Given Boolean expression: AB' + AB + A'B

Step-by-step simplification:

Step 1: Take common factor from first two terms
AB' + AB = A(B' + B) Applied Law: Distributive Law [XY + XZ = X(Y + Z)]

So the expression becomes:
A(B' + B) + A'B

Step 2: Simplify ((B' + B))
B' + B = 1 Applied Law: Complement Law [ X + X' = 1 ]

Therefore:
A(1) + A'B

Step 3: Simplify (A(1))
A . 1 = A Applied Law: Identity Law [ X . 1 = X ]

Now expression becomes:
A + A'B

Step 4: Simplify (A + A'B)
A + A'B = A + B Applied Law: Absorption Law / Redundancy Theorem [ X + X'Y = X + Y ]

Hence:

AB'+AB+A'B=A+B

Final Answer: A + B