I am having trouble with "and" , "or" in my formulas.

If I want one of c1:c4 to be true is this the formula to use
=if((c1:c4)>d1),g1,"") or should I use =if(or(c1:c4)>d1),g1,""). Neither one
of these formulas seems to work. In other words, I am trying to write a
shorter formula for the following:

=if(c1>d1 or c2>d1 or c3>d1 or c4>d1, G1,"")

Thanks for help with this simple formula.