The following predicate logic formula is invalid:

[(,)][(,)]

Within 4 new text cells indicate which of the following are counterexamples for this formula, and briefly explain your choice.

1. The predicate (,):=1 where the domain is the rational numbers .
2. The predicate (,):< where the domain is the real numbers .
3. The predicate (,):=2 where the domain is the real numbers without 0 symbolized as {0}.
4. The predicate (,):= where the domain of discourse is the set of all binary strings, including the empty string.