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

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

A

`max(p, q) lt max (p, q, r)`

B

`min (p, q) = (1)/(2) (p + q - | p -q |)`

C

`max ( p, q) lt min (p, q , r)`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
Since, max `(p, q) = {{:( p",",, if p gt q ), ( q",",, if q gt q):}`
and `max ( p, q, r) = {{:( p",",, if p" is greater "), (q", " ,, if q " is greatest " ) , (r",",, if r " is greatest " ):}`
`therefore max (p, q) lt max ( p, q, r) ` is false.
We know that, ` |p - q| = {{:( p-q",",, if p ge q ), ( q-p"," ,, if p lt q ) :}`
`therefore (1)/(2) ( p + q - |p - q | ) = {{:((1)/(2)( p + q - p+ q )",",, if p ge q ), ( (1)/(2) ( p + q + p - q)"," ,, if p lt q ):}`
`" " = {{:( q",",, if p ge q ), ( p ",",, if p lt q ):}`
`rArr (1)/(2){ p +q - | p -q| } = min ( p, q)`
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