The contrapositive of a proposition is formed by two steps:
1. Switching the subject and predicate terms, as in taking the
2. Replacing both the subject and the predicate terms with their
The quality and quantity of the proposition remain as they were.
It is always legitimate to take the contrapositive of an A
proposition. An A proposition says that the class of Ss is
included within the class of Ps. So anything outside the class
of Ps (i.e., all the non-Ps) must be outside the class of Ss
(i.e., it must be a non-S).
Switzerland is in Europe, so if you're not in Europe, you're not
Contraposition is not a legitimate operation for I and E
The E proposition, "No primate is an aquatic animal," is clearly
not equivalent to its contrapositive, "No nonaquatic animal is a
nonprimate," because the first is true and the second false (cows
are nonaquatic animals but they are nonprimates).
Similarly, the I proposition, "Some soldiers are nonofficers," is
clearly not equivalent to its contrapositive, "Some officers are
The O proposition is the only one, besides the A, that is
equivalent to its contrapositive. Even so, it is rarely used in