Question

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

If Pam lives in Chicago, then she lives in Illinois.

Short answer

The statement "If Pam lives in Chicago, then she lives in Illinois" is true.

The converse of the given statement “If Pam lives in Illinois, then she lives in Chicago” is false.

Step-by-step solution

Step 1. Converse of a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement “If p, then q” will be “If q, then p”.

Step 2. State whether the statement is true or not.

In the statement "If Pam lives in Chicago, then she lives in Illinois", it is given that Pam lives in Chicago. And Chicago is in Illinois. Therefore, Pam lives in Illinois.

Hence, the statement is true.

Step 3. Write the converse.

Consider p is "Pam lives in Chicago" and q is "she lives in Illinois".

The converse is of the form "if q, then p”.

Therefore, the converse of the given statement is – “If Pam lives in Illinois, then she lives in Chicago.”

Step 4. State whether the converse is true or not.

In converse, it is given that Pam lives in Illinois but there are other places than Chicago in Illinois.

Therefore, she can live anywhere in Illinois other than Chicago.

Therefore, the converse of the given statement is false.