4.3 Operations on Statements (Part 3)
(C) Truth Values of Compound Statements using ‘Or’
1. When two statements are combined using ‘or’, a false compound statement is obtained only if both statements are false.
2. f one or both statements are true, then the compound statement is true.
The truth table:
Let p = statement 1 and q= statement 2.
The truth values for ‘p’ or ‘q’ are as follows:
Example 6:
Determine the truth value of the following statements.
(a) 60 is divisible by 4 or 9.
(b) 53 = 25 or 43 = 64.
(c) 5 + 7 > 14 or √9 = 2.
Solution:
(a)
60 is divisible by 4 ← (p is true)
60 is divisible by 9 ← (q is false)
Therefore, 60 is divisible by 4 or 9 is a true statement. (‘p or q’ is true)
(b)
53 = 25 ← (p is false)
43 = 64 ← (q is true)
Therefore, 53 = 25 or 43 = 64 is a true statement. (‘p or q’ is true)
(c)
5 + 7 > 14 ← (p is false)
√9 = 2 ← (q is false)
Therefore, 5 + 7 > 14 or √9 = 2 is a false statement. (‘p or q’ is false)