### “A and B” is equivalent to “B and A”, and the order matters

In math, I’m used to making no distinction between saying “A and B” and saying “B and A” — they each assert that both of the component statements are true. In fancy terms, we say that the conjunction “and” is commutative, like addition (a+b=b+a) and multiplication (ab = ba). Many mathematical operations are not commutative in general, like subtraction (a–b ≠ b–a), or matrix multiplication (AB ≠ BA). I’ve noticed that the way we use “and” in regular speech, there’s a subtle difference between saying “A and B” and saying “B and A” — here, take a look at the difference between these two examples:

• “There are things you can do to improve your personal situation, and some problems are structural and need to be addressed at the societal level.”
• “Some problems are structural and need to be addressed at the societal level, and there are things you can do to improve your personal situation.”

These both express the same two truths, but they feel very different. The first I could imagine saying to someone who is all about self-help and needs to be reminded of the importance of collective action, while the second would be more appropriate for someone feeling so discouraged by life’s injustices that they need to be reminded of their own agency. (I’ve been both of these people.)

Or try these:

• “Sometimes you need to pause and take care of yourself, and sometimes you need to get right back out there.”
• “Sometimes you need to get right back out there, and sometimes you need to pause and take care of yourself.”

These are logically equivalent, but the speaker seems to be suggesting the second option in each case. It looks like the pattern when saying “A and B”, if A and B are two ideas in tension with each other, is that “A” is the idea more in line with the listener’s current thoughts, and “B” is the idea that the speaker wants to add to the conversation.

Are there ideas in tension that you have to take turns reminding yourself of? Other situations where the order you say things makes a difference? I’d love to hear from you in the comments!