NIMCET 2014 — Computer PYQ
NIMCET | Computer | 2014The Boolean expression X(X+Y) is same as:
Choose the correct answer:
- A.
X⋅(1+Y)
- B.
X
- C.
X⋅1
- D.
All of these
(Correct Answer)
All of these
Explanation
Solving
Expression: X(X+Y)
Step 1: Distributive Law
X⋅X+X⋅Y
Step 2: Idempotent Law (X⋅X=X)
X+X⋅Y
Step 3: Factor out X
X(1+Y)
(This matches Option 1)
Step 4: Identity Law (1+Y=1)
X(1)
(This matches Option 3)
Step 5: Final Simplification
X
Result: Since all forms are mathematically equivalent in Boolean algebra, the answer is 4. All of these.
Explanation
Solving
Expression: X(X+Y)
Step 1: Distributive Law
X⋅X+X⋅Y
Step 2: Idempotent Law (X⋅X=X)
X+X⋅Y
Step 3: Factor out X
X(1+Y)
(This matches Option 1)
Step 4: Identity Law (1+Y=1)
X(1)
(This matches Option 3)
Step 5: Final Simplification
X
Result: Since all forms are mathematically equivalent in Boolean algebra, the answer is 4. All of these.