Foundations, part 3

Algebra Level pending

\[\begin{align} P\left(x,y,z\right) & = \max\left(x,y\right) + \min\left(y,z\right) \\ Q\left(x,y,z\right) & = \max\left(y,z\right) + \min\left(x,y\right) \\ R\left(x,y,z\right) & = \max\left(x,y,z\right) \\ S\left(x,y,z\right) & = \min\left(x,y,z\right) \\ T\left(x,y,z\right) & = \max\left(x,z\right) - \min\left(y,z\right) \\ U\left(x,y,z\right) & = \max\left(y,z\right) - \min\left(x,y\right) \end{align} \]

Functions \(P\), \(Q\), \(R\), \(S\), \(T\), and \(U\) are defined as above, where \(\max\left(a,b,\cdots\right) = \) largest of all numbers and \(\min\left(a,b,\cdots\right) = \) smallest of all numbers.

For \(x = 1\), \(y = 2\), and \(z = 3\), which of the options is less than 1?

For more, try this set.

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