Billing Statement

I am trying to write out the negations of the definitions of upper and lower bounds and I cant remember how to write the negation of a biconditional statement.
The statements I have to negate are

Suppose S is a subset of Real numbers.
A number u in R is an upper bound if and only if for every s in S, s is less than or equal to u.

A number Z in R is a lower bound for s if and only if for every s in S, l is less than or equal to s.

P iff Q is equivalent to: (if P then Q) and (if Q then P). The negation of this is: not(if P then Q) or not(if Q then P). That last is equivalent, via contrapositives, to: (Q and notP) or (P and notQ).

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