Question

Value of $Ma \left[ md(a), \ mn(md(b), a), \ mn(ab, md(ac)) \right]$ where $a = -2$, $b = -3$, $c = 4$ is:

• A. 2
• B. 6
• C. 8
• D. -2

Hint:

When applying min and max functions, compute inner absolute values first, then min/max step-by-step to avoid sign confusion.

Answer 1

The Correct Option is C

We are given the definitions:
- $md(x) = |x|$ (absolute value)
- $mn(x, y)$ = minimum of $x$ and $y$
- $Ma(a, b, c, \dots)$ = maximum of $a, b, c, \dots$
First, calculate each term:
1. $md(a) = |-2| = 2$.
2. $md(b) = |-3| = 3$. Then $mn(md(b), a) = mn(3, -2) = \min(3, -2) = -2$.
3. $ab = (-2) \times (-3) = 6$.
$ac = (-2) \times (4) = -8$, so $md(ac) = |-8| = 8$.
Then $mn(ab, md(ac)) = mn(6, 8) = \min(6, 8) = 6$.
Now apply the $Ma$ function:
$Ma[ md(a), \ mn(md(b), a), \ mn(ab, md(ac)) ] = Ma[ 2, \ -2, \ 6 ] = \max(2, -2, 6) = 6$. Wait — that gives 6, not 8. Let's recheck carefully.
Actually, check step 3 again: $ab = (-2) \times (-3) = 6$, $md(ac) = |-8| = 8$, so $mn(6, 8) = 6$. That’s correct.
Thus maximum of $(2, -2, 6)$ = $6$.
Hence final answer is $\boxed{6}$, so the correct choice is (B).