GATE CS 2008 Q18 — Programming in C

The given expression uses nested ternary operators:

$$a = (x > y) ? ((x > z) ? x : z) : ((y > z) ? y : z)$$

Let's analyze the logic of this expression step-by-step:

1. If $x > y$ is true:

   The expression evaluates to (x > z) ? x : z, which returns the maximum of $x$ and $z$. Since $x > y$, this effectively returns the maximum of all three variables, $\max(x, y, z)$.

2. If $x > y$ is false (i.e., $x \le y$):

   The expression evaluates to (y > z) ? y : z, which returns the maximum of $y$ and $z$. Since $y \ge x$, this also returns the maximum of all three variables, $\max(x, y, z)$.

Thus, the expression simplifies to finding the maximum of the three variables:

$$a = \max(x, y, z)$$

We want $a = 4$. Let's evaluate the options to find which set of values has a maximum of $4$:

• Option A: $x=3, y=4, z=2 \implies \max(3, 4, 2) = 4$. (Correct)
• Option B: $x=6, y=5, z=3 \implies \max(6, 5, 3) = 6$.
• Option C: $x=6, y=3, z=5 \implies \max(6, 3, 5) = 6$.
• Option D: $x=5, y=4, z=5 \implies \max(5, 4, 5) = 5$.