Question

Select correct truth table. 

• A.
• B.
• C.
• D.

Hint:

Always simplify the Boolean expression first, then prepare the truth table for accuracy.

Answer 1

The Correct Option is D

Step 1: Simplification using Boolean algebra laws

From the given logic circuit, the output expression can be written as:

Y = (A · B) · A

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Using De Morgan’s theorem:

(A · B) = A + B

Substituting,

Y = ( A + B ) · A

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Applying distributive law:

Y = AA + AB

Since,

AA = 0

Therefore,

Y = AB

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Step 2: Verification using Boolean conditions

The expression Y = AB is true only when:

• A = 1
• B = 0

For all other input combinations, the output is zero.

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Step 3: Truth table verification 

A	B	Y
0	0	0
0	1	0
1	0	1
1	1	0

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Final Answer:

The given logic circuit represents the Boolean expression 
Y = AB, 
which corresponds to option (4).