Question

For $x = 15, y = 10, z = 9$, find the value of le$\big(x, \min(y, x-z), \ \text{le}(9, 8, \text{ma}(x, y, z))\big)$.

• A. 5
• B. 12
• C. 9
• D. 4

Hint:

Carefully evaluate inner functions before substituting into the outer one — especially when multiple mins and maxes are involved.

Answer 1

The Correct Option is A

First, compute ma$(x, y, z) = \frac{1}{2}[\text{le}(15, 10, 9) + \text{la}(15, 10, 9)]$. le$(15, 10, 9) = \max(15-10, 10-9) = \max(5, 1) = 5$. la$(15, 10, 9) = \min(15+10, 10+9) = \min(25, 19) = 19$. So ma$(15, 10, 9) = \frac{1}{2}(5 + 19) = \frac{24}{2} = 12$. Now compute le$(9, 8, 12) = \max(9-8, 8-12) = \max(1, -4) = 1$. Next, $\min(y, x - z) = \min(10, 15 - 9) = \min(10, 6) = 6$. Finally, le$(15, 6, 1) = \max(15 - 6, 6 - 1) = \max(9, 5) = 9$. Wait — the calculation needs check: We have le$(x, \min(y, x-z), \ \text{le}(9, 8, \text{ma})) = \text{le}(15, 6, 1) = \max(15 - 6, 6 - 1) = \max(9, 5) = 9$. This yields option (c) instead of (a).