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The expression max(a,b) means the larger of a and b.  If x > y > z, then x + y + z - max(x,y) - max(x,z) - max(y,z) + max(x,y,z) always equals one of x, y, or z.  Determine which one.

 Dec 18, 2019
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Since x > y > z   (meaningx is the largest , y is the second largest, and z is the smallest of the three quantities), then

 

max(x, y) = x          (since x is the largest),

max(x, z) = x          (since x is the largest),

max(y, z) = y           (since y is the second largest) , and

max(x, y, z) = x      (since x is the largest).

 

so x + y +z - max(x.y) - max(x, z) - max(y, z) +max(x, y, z) =  x + y + z - x - x - y + x = 2x - 2x +y - y +z =  z . So z remains because he is the smallest.

 Dec 20, 2019

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