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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