three lights, two switches

You could use DPST switches but I'd just put B on a pair of SPDT switches and put a and b on their own SPST switches.

Nope, that would not work as a so called 3-way switch is single pole DOUBLE throw.

To do what the OP desires would actually take two DPDT switches.

B would be a standard 3way hook up A and B would just require the spst terminals

though such switches are very common (as a toggle switch) as a wall switch for a house I have never seen such a thing. Probably could get one somewhere but your average hardware store would not have it...possibly an industrial supply house

The easy way is to put a fixture with 2 lamp holders in the B position and wire one to A and the other to C. If you are willing to run a lot of wire I imagine we can come up with a way of doing it with one light in B

COrrection:

This seems to be the best solution

the one I offered would not only require a special switch I realized after I posted that there would be no way to have all lights on or all lights off at the same time. In other words... useless.

Would using a dimmer switch help somehow? If, say, the OP's end goal is to vary the light level?

I agree, your initial idea, I initially thought would work too. But you wind up with a 3-way switch on one pole and essentially a SPST on the other, so while you can control the lights, you still can't get them to do what you want if the other switch is in the other position. I don't see a way of doing it just with two switches.

Yep.

Unless one wanted to use relays and design a logic circuit, the only practical way would be to use two bulbs at location "B"

That way a three-way switch at each end could be used

Bulb A tied to B(a) Bulb C tied to B(b)

LOL. should have thought about that first.... No option for all off.

two switches is the way to go I think

I would accomplish the same thing by using double-pole switches rather than 2 lights at B. One pole of each switch for B, the other for A or C.

Note that neither is the same as 3-way. In one of these setups, you get light at B if EITHER switch is on (1 OR 2). In a 3-way, you get light only when the switches are in DIFFERENT positions (1 XOR 2).

That would be strange. Consider what happens when you operate switch 1. You get either:

Switch 1 turns lights A and B on/off together.

OR

Switch 1 switches between the lights (A on / B off) and (A off / B on).

Depending on the state of switch 2.

I may be confused about which way that is (I think double-pole double-throw switches with one pole used as 3-way). One combination has all 3 lights off, the others have TWO lights on. These is no combination for ONE light on, or all on.

That is, all off, A and B on, B and C on, A and C on.

The other way has all off, A and B on, B and C on, all on.

The difference is if turning A and C on will turn B on or off.

As for B, it's the same difference as between the logic functions OR and XOR (exclusive-or), which made this easier to understand.

So now you have 4 bulbs, in 2 parallel connections. Both 3-way? Now you have FOUR switches.

Or do you use regular switches? That might be the way I choose (although I'd still prefer the DP switches). It's not 3-way.

Thanks to all who replied to my question. I didn't realize this would be so involved. I thought it was just a simple wiring problem.

If there are two bulbs at B, wouldn't two single pole switches do the job, one for A, B(a), the other B(b), C?

Not to vary the light level. My actual situation is a little more complex than what I have posted.

This is for bathroom. I want to have one light each above vanity, shower stall, and commode while at the same time a common light for the whole bathroom.

What made a seemingly simple question complicated was that you said you wanted "B" controlled by two switches.

If you have two bulbs at"B" then a single pole switch indeed could control A and B(a) and the second single pole switch could control B(b) and C

Yep, after I posted solutions I realized I was wrong.

I think it may be all sorted out now

Yes I messed up a bit

Years ago I was good at logic and could do it again if I thought a little harder

You can certainly use 2 pole switches and run 2 extra wires to "B" and "C" to avoid the parallel neutral violation. The "B" side of the switch at "C" would be on a loop. There are other options but it still ends up being a lot of extra wire. That is particularly true after 2014 when a neutral is required at each switch location