A disjunction is a compound statement formed by joining two statements with the connector. A disjunction is false if and only if both statements are false; otherwise it is true.
Example 3:
Given: r: x is divisible by 2.
s: x is divisible by 3.
Problem: What are the truth values of rs?
Solution: Each statement given in this example represents an open sentence, so the truth value of rs will depend on the replacement values of x as shown below.
If x = 6, then r is true, and s is true. The disjunction rs is true.
If x = 8, then r is true, and s is false. The disjunction rs is true.
If x = 15, then r is false, and s is true. The disjunction rs is true.
If x = 11, then r is false, and s is false. The disjunction rs is false.
