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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?

  1. $la(x,y,z) < le(x,y,z)$ 
  2. $ma(x,y,z) < la(x,y,z)$ 
  3. $ma(x,y,z) < le(x,y,z)$
  4. None of these
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