For each of the following statements, put it into proper categorical form and say whether it is A, E, I, or O; then form the obverse of the statement.
For each of the following statements, (a) put it into categorical form and then (b) form the converse and the contrapositive. (c) State whether the converse and the contrapositive are logically equivalent to the original in each case. (Use the A, E, I, O labels, and use letters for the formal representation of categories. For instance, “All humans have backbones” would be “All H are B,” where H represents the category of humans and B represents the category of creatures with backbones. The converse would be “All creatures with backbones are humans” (All B are H), which is a statement of the A form. The contrapositive would be “All noncrea- tures with backbones are nonhumans” (All non-B are non-H), which is also a statement of the A form. The converse of the original statement is not logically equivalent to it, but the contra- positive is logically equivalent to it.)
For each of the following statements, put the statement into categorical form and then form the contradictory. For example, “Some stinging creatures are bees” is an I statement, and may be represented as “Some S are B.” The contradictory of an I statement is an E statement with the same subject and predicate; thus the contradictory of “Some S are B” is “No S are B.”
4. Some teachers are well paid.
7. All philosophers explore questions of meaning.