Final answer:
The statement 'A poet is a writer' is explored by creating an if-then form, its converse, inverse, and contrapositive, which help examine the relationship between the elements of the statement in logical terms, with the contrapositive being equivalent to the original statement.
Step-by-step explanation:
The statement 'A poet is a writer' can be transformed into different logical forms. We will discuss the if-then form, the converse, the inverse, and the contrapositive:
If-then form: If someone is a poet, then that person is a writer.
Converse: If someone is a writer, then that person is a poet.
Inverse: If someone is not a poet, then that person is not a writer.
Contrapositive: If someone is not a writer, then that person is not a poet.
In logic, these transformations help us understand the relationship between different elements within a statement by rearranging the hypothesis and conclusion. The contrapositive is unique because, in logical terms, it is always equivalent to the original if-then statement, whereas the converse and the inverse may not necessarily be true.