For these questions, the following functions have been defined:
$la(x,y,z) = min(x+y, y+z)$
$le (x,y,z) = max(x–y, y–z)$
$ma(x,y,z)=(1/2) [le(x,y,z)+la(x,y,z)]$
Given that $x > y > z > 0$, which of the following is necessarily true?
- $la(x,y,z) < le(x,y,z)$
- $ma(x,y,z) < la(x,y,z)$
- $ma(x,y,z) < le(x,y,z)$
- None of these