Exercise 22 Page 103

Using the given statements and the map, we will write a compound statement and determine its truth value. In this case, our compound statement will be a disjunction because it involves the sign "$\vee .$" Let's look at the map and the statements.

• $p$: Springfield is the capital of Illinois.
• $q$: Illinois borders the Atlantic Ocean.
• $r$: Illinois shares a border with Kentucky.
• $s$: Illinois is to the west of Missouri.

Now, we can write our compound statement. Notice that we have the negation of statement $s$ and statement $p.$ The negation of a statement has the opposite meaning, as well as an opposite truth value. We need to remember that a disjunction is true if at least one of the statements is true. Thus, we will first determine the truth value of statement $\neg s$ and statement $\neg p.$

Statement	Truth Value
$\neg s:$ Illinois is not to the west of Missouri.	True
$\neg p$: Springfield is not the capital of Illinois.	False

Since at least one of the statements is true, the disjunction is also true.