Which of the following truth table is true?

Moderate

A

$\begin{array}{l} A & B & Υ \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{array}$
B

$\begin{array}{l} A & B & Υ \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{array}$
C

$\begin{array}{l} A & B & Υ \\ 0 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{array}$
D

$\begin{array}{l} A & B & Υ \\ 0 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{array}$

Solution

Let A = 0 & B = 0 Let A = 0 & B = 1
$Υ = (A \cdot \bar{B}) (\bar{A} \cdot B) Υ = (A \cdot \bar{B}) (\bar{A} \cdot B) = (0. \bar{0}) (\bar{0} .0) = (0. \bar{1}) (\bar{0} .1) = (0.1) (1.0) = (0.0) (1.1) = (0) (0) = (0) (1) = 0 = 0$
Let A = 1 & B = 0 Let A = 1 & B = 1
$Υ = (A \cdot \bar{B}) (\bar{A} \cdot B) Υ = (A \cdot \bar{B}) (\bar{A} \cdot B) = (1. \bar{0}) (\bar{1} .0) = (1. \bar{1}) (\bar{1} .1) = (1.1) (0.0) = (1.0) (0.1) = (1) (0) = (0) (0) = 0 = 0 \begin{array}{l} A & B & Υ \\ 0 & 0 & 0 \\ 1 & 0 & 0 O p t i o n 1 i s C o r r e c t \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{array}$

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