Find the truth table for the function Y of A and B represented in the following figure.
Find the truth table for the function Y of A and B represented in the following figure.
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A
B
C
D
The Correct Option is C
Solution and Explanation
From the given logic circuit:
The upper gate is an AND gate with inputs $A$ and $B$. \[ \text{Output}_1 = A \cdot B \]
The lower branch takes input $B$ through a NOT gate. \[ \text{Output}_2 = \overline{B} \]
These two outputs are connected to an OR gate.
Hence the output function is: \[ Y = (A \cdot B) + \overline{B} \] Now simplify using Boolean algebra: \[ (A \cdot B) + \overline{B} = (A + \overline{B})(B + \overline{B}) \] Since: \[ B + \overline{B} = 1 \] \[ Y = A + \overline{B} \] Truth Table for $Y = A + \overline{B}$ 
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