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Matching Or expressions


The context of my problem is explained below.

I wish to distinguish expressions of the form And[p,q] from those of the 
form Or[p,q], but the only thing I find is
MatchQ[myExpr, Or[_]]
and to my surprise I see that MatchQ[And[p,q],Or[_]] is True. Thus I can 
not use this to match only the Or-expressions.

Thanks

Johan

The context is as follows:

I wish to find the number of solutions to a  diophantine equation with a 
finite number of solutions.

I do the following
sols = Reduce[eqns, vars, Integers]
and this gives me an expression that normally looks like Or[_,_,_] if 
there are several solutions, or something else if there are not.

Now I wish to find the number of solutions using
Which[MatchQ[sols, Or[_]], Length[sols], DoOtherStuff]

The problem is that the MatchQ[ expr, Or[_] ] also matches e.g. (x==2 && 
y==4), which is only one solution.


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