[AccessD] finding duplicates among different departmental programs

I created a program, about a year and a half ago, for an agency that
deals with providing programs for the elderly. This agency gets its
funding from many different sources and a single source may fund
multiple programs. To track all of this we need to provide many stats.

When this was written, there wasn't a concern about a person being in
multiple programs, although I warned about it. Now, because there state
reporting has changed, there may be a concern. The state is kicking back
their reports because one of their funding counts is greater than the
total amount of participants; there are 1236 people enrolled with the
agency, but one group of programs is showing a count of 1257. I think
the fact that they are even close is a coincidence...I took a sample of
13 members and all but four were in at least 2 of the programs, and
actually my queries, out of necessity, each handle two programs (there
are four for this group) and each one blocks out its own 'duplicates',
so it is very conceivable that many of these people are in all four of
the groups.

Question:

qryOne looks for people in Prog1 OR Prog2 (count = 809)
qryTwo looks for people in ProgA OR ProgB (count = 410)

I need a total count of those is qryOne OR qryTwo 

*** I don't want those that are in both counted twice, which is what a
count of 1219 (809 + 410) 
will give me.

I'm thinking that I need to use one of these queries into another
query...???

Thanks in advance for any help!