"The Average Person's Axioms of First Order Predicate Logic:
(A -> B) -> (B -> A)
(There exists) x A(x) -> (For all) x A(x)
(A -> C) AND (B -> C) -> (A -> B)
Predicate logic is the study of why the above is funny."
Or, in English:
If a duck is an animal, then an animal is a duck.
There is a toy that is red, therefore all toys are red.
If it rains the ground will be wet, and if the sprinklers turn on the ground will be wet, therefore if it rains the sprinklers will turn on.