Question

If $p,q,r$ are any real numbers, then

• A. max $(p,q)$ < max $(p,q,r)$
• B. min $(p,q)=$$\frac{1}{2}$ $(p+q-|p-q|)$
• C. max $(p,q)$ < min$(p,q,r)$
• D. None of these

Answer 1

The correct option is B min $(p,q)=$$\frac{1}{2}$ $(p+q-|p-q|)$

$p,q,r\in R$

(A) $max(p,q)<max(p,q,r)$ it depends of $p,q,r$

(B)$min(p,q)=\frac{1}{2}(p+q-|p-q|)$

Let $p,q$ be $1,2,\Rightarrow min(1,2)=\frac{1}{2}(1+2-|1-2|)$

$1=\frac{1}{2}(3-1)$

$1=\frac{1}{2}\left(2\right)$

$1=1$identity.

$\Rightarrow$ (B) is right.