Final answer:
The conditional statement 'If a person lives in Paris, then they live in France' is true. Its converse 'If a person lives in France, then they live in Paris' and inverse 'If a person does not live in Paris, then they do not live in France' are false, while the contrapositive 'If a person does not live in France, then they do not live in Paris' is true.
Step-by-step explanation:
The statement 'A person lives in Paris and lives in France' can be expressed in conditional form and then transformed into its converse, inverse, and contrapositive forms. Let's use 'P' to represent 'A person lives in Paris' and 'F' to represent 'A person lives in France.'
Conditional Statement
If P, then F. This is the original form of the statement, expressing that if the condition of living in Paris is true, then living in France is necessarily true. Its truth value is true, since Paris is a city within France.
Converse
If F, then P. The converse swaps the hypothesis and the conclusion. This statement's truth value is false, since one can live elsewhere in France and not only in Paris.
Inverse
If not P, then not F. The inverse negates both the hypothesis and the conclusion. This statement's truth value is also false because one could live in other areas of France, outside of Paris.
Contrapositive
If not F, then not P. The contrapositive negates and swaps the hypothesis and conclusion of the original conditional. The truth value of the contrapositive is true, as it is logically equivalent to the original conditional statement; if one does not live in France, then they cannot be living in Paris.