Wire a bathroom fan and light so the light always controls the fan, but the fan can be operated independantly from the light

Question

I have a bathroom light fixture and a fan that are currently both independently controlled by their own switches. I'd like to wire it (preferably without having to go into the attic to change the current wiring...asbestos insulation) such that when the light comes on, the fan also comes on, but the fan can be operated independently.
Truth Table of desired effect
+--------------+------------+-------+-----+
| Light Switch | Fan Switch | Light | Fan |
+--------------+------------+-------+-----+
| Off          | Off        | Off   | Off |
| Off          | On         | Off   | On  |
| On           | Off        | On    | On  |
| On           | On         | On    | On  |
+--------------+------------+-------+-----+

The current wiring is like this for both switches.

I was thinking that there has to be some way to wire the switches together with 3 or 4-way switches in order to acheive the desired effect, but I am having trouble coming up with a solution. Thoughts?

George Anderson · Accepted Answer

You could do that with a double pole switch and a single pole normal switch.  Wire the hot to both of the line side poles on the double pole switch as well as to the single pole switch.
Wire both the fan and the light to individual poles on switched side of the double pole switch.  Then run a jumper from the pole that controls the fan on the double pole switch to the switched side of the single pole switch.  All the neutrals and grounds stay connected as they are. Don't get confused with a 3-way or 4-way switch, those are different animals.  You may have to go to an electrical supply house to get a true double pole wall switch.
I could provide a diagram if you want.   But I want to post this quickly to beat out the big 3!  LOL  Competition for points here is fierce!  LOL

Carl asked me to provide more info.  This what I have time for right now. If others wanted to contribute a better diagram, that's welcome.

Wire a bathroom fan and light so the light always controls the fan, but the fan can be operated independantly from the light

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