I'm browsing through the introduction section of Folland's Real Analysis: Modern Techniques and Their Applications, and I've read a claim that I can't make sense of:
[...] a partial ordering on $X$ naturally induces a partial ordering on every nonempty subset of $X$.
What is the construction of such a naturally induced partial ordering? And what is a non-trivial example of this partial ordering on subsets of $X$? (I have a sense that this is the sort of idea that may be obvious in hindsight.)
Edit:
I misunderstood the claim. I was thinking that given some partial ordering on, say, the set $X = \{a, b\}$ that there was a naturally induced partial ordering on the set $X' = \{\{a\}, \{b\}, \{a, b\}\}$.