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 " $\lor .$ " 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.

\underline{\neg s \lor \neg p} Illinois is not to the west of Missouri or Springfield is not the capital of Illinois .

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.

Exercise

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