Foundations, part 3

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

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 .