Can "any of" be followed by "and" or must it be "or"

Actually, the intent of the paragraph is to divide the residue among those of the named group who survive my death, except for a situation where one or more of the group has predeceased leaving a child or children alive at my death - in that circumstance the child or children would take the parent's share.

Initially though my question was whether to use 'and' or 'or' after the statement 'if any of ____, _____, and / or _____.

I agree with JSW 29 because they are a set.