GATE CS 2012 Q.6 (CS Q.6): Boolean Algebra and Logic Minimization

The truth table

\begin{array}{cc|c} X & Y & f(X, Y) \\ \hline 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 1 \end{array}

represents the Boolean function

$X$

$X + Y$

$X \oplus Y$

$Y$

Official answer and solution

Official answer: A
From: Official GATE 2012 answer key

Solution

Compare the output column of the truth table with the input columns X and Y.

Examine the given truth table:

\begin{array}{cc|c} X & Y & f(X, Y) \\ \hline 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 1 \end{array}

Notice that whenever $X = 0$ , $f(X, Y) = 0$ , and whenever $X = 1$ , $f(X, Y) = 1$ , regardless of the value of $Y$ .
Thus, the function value is entirely determined by $X$ :

f(X, Y) = X

This matches option (A).

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2012 Computer Science and Information Technology (CS)
Question: 6 of 65, printed as CS Q.6
Section: Computer Science and Information Technology

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