GATE CS 2012 Q6 — Boolean Algebra

To find the Boolean function represented by the given truth table, let us analyze the output column $(X, Y)$ for each combination of inputs $X$ and $Y$:

• When $X = 0, Y = 0$, the output is $0$.
• When $X = 0, Y = 1$, the output is $0$.
• When $X = 1, Y = 0$, the output is $1$.
• When $X = 1, Y = 1$, the output is $1$.

Comparing the output column with the input columns, we can see that the output is always identical to the value of $X$, regardless of the value of $Y$.

Mathematically, we can write the sum-of-products (SOP) expression as:

$$f(X, Y) = X\bar{Y} + XY = X(\bar{Y} + Y) = X(1) = X$$

Therefore, the truth table represents the Boolean function $X$, which corresponds to option A.