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 Logicians use the terms conversion, obversion, and contraposition to define three types of logically equivalent statements, but we will not need to memorize these terms. Below are listed on the right the only logically equivalent statements to those on the left:

Some logically equivalent statements seem cumbersome and overloaded with negatives. That apparent weakness is a strength of the concept of logical equivalence, for we may encounter a statement on the right and want to translate it into a familiar classification statement.

The concept of logical equivalence can also be useful in experimental design. For example, it might be impossible to show that ‘some S are P’ but easy to show that ‘some P are S’. In Chapter 7 we will consider the Raven’s Paradox: the two statements ‘All ravens are black’ and ‘All nonblack things are non-ravens’ may be logically equivalent, but testing the latter would involve an inventory of the universe.

For recognizing logically equivalent statements, substitution is an alternative to Venn diagrams. For example, replace S with scientists and replace P with either people, physicists, or politicians, whichever gives a true initial statement:

Valid equivalent statements:

Non-equivalent statements: