The following operations are defined for any two real numbr p and q.
`mn(p, q)="min "(p, q)`
`mx(p, q)=" max "(p,q)`
`md(p)=|p|`
Find the value of `md(mn(P, mx(md(q),mn(p, r)))),p=-2, q=5,r=7`.

Options

A. A. `-1`
B. B. 0
C. C. 2
D. D. none of these

Answer

To solve the problem step by step, we will follow the operations defined for the real numbers \( p \), \( q \), and \( r \) as specified in the question.

Given:
- \( p = -2 \)
- \( q = 5 \)
- \( r = 7 \)

We need to evaluate:
\[ md(mn(p, mx(md(q), mn(p, r)))) \]

### Step 1: Calculate \( mn(p, r) \)
We first find the minimum of \( p \) and \( r \):
\[ mn(p, r) = \min(-2, 7) = -2 \]

### Step 2: Calculate \( md(q) \)
Next, we calculate the modulus of \( q \):
\[ md(q) = |q| = |5| = 5 \]

### Step 3: Calculate \( mx(md(q), mn(p, r)) \)
Now, we need to find the maximum of \( md(q) \) and \( mn(p, r) \):
\[ mx(md(q), mn(p, r)) = mx(5, -2) = \max(5, -2) = 5 \]

### Step 4: Calculate \( mn(p, mx(md(q), mn(p, r))) \)
Next, we find the minimum of \( p \) and the result from the previous step:
\[ mn(p, mx(md(q), mn(p, r))) = mn(-2, 5) = \min(-2, 5) = -2 \]

### Step 5: Calculate \( md(mn(p, mx(md(q), mn(p, r)))) \)
Finally, we apply the modulus to the result from the previous step:
\[ md(mn(p, mx(md(q), mn(p, r)))) = md(-2) = |-2| = 2 \]

### Final Answer
Thus, the value of \( md(mn(p, mx(md(q), mn(p, r)))) \) is \( 2 \).

---