Readings & Meanings:
to be mixed, to be associated with
To show we were friends, we shook hands.
Let's stick to the rules of traffic.
I feel that there's a problem with the government's foreign policy.
I made friends with the exchange student from Singapore.
Another cover radical, 亠, is the Nabe-buta, the Nabe lid radical.
We've seen this a couple of times or so.
We've essentially got a cross-legged person here. Yes, it looks like the Dad kanji, 父. Kanji networks says that's just a coincidence.
So, cross-legged person -> cross, interchange, mix, mingle, converse.
交 is also a frequently-used element itself; see, for example, 学校.