McGraw Hill Glencoe Geometry, 2012
MH
McGraw Hill Glencoe Geometry, 2012 View details
2. Logic
Continue to next subchapter

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 "" Let's look at the map and the statements.

  • : Springfield is the capital of Illinois.
  • : Illinois borders the Atlantic Ocean.
  • : Illinois shares a border with Kentucky.
  • : Illinois is to the west of Missouri.
Now, we can write our compound statement. Notice that we have the negation of statement and statement 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 and statement
Statement Truth Value
Illinois is not to the west of Missouri. True
: Springfield is not the capital of Illinois. False

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