GATE2012-6

Question

The truth table ${\begin{array}{|c|c|c|}\hline
\textbf{X}&    \textbf{Y}&  \textbf{(X,Y)} \\\hline
0&    0&   0 \\ \hline   
0&     1&0\\     \hline
1&   0&  1     \\\hline
1&    1& 1     \\\hline
\end{array}}$ represents the Boolean function

• A. $X$
• B. $X + Y$
• C. $X \oplus Y$
• D. $Y$

Answer 1

Whenever $X$ is true $(X,Y)$ is true and whenever $X$ is false $(X,Y)$ is false, so the answer is (A) $X$.

Answer 2

f(x,y)= xy' + xy
        = x(y'+y)
        = x

Answer 3

Using $k-$map method,we get $f(x,y) = x.$