4.3 Operations on Statements (Part 2)
(B) Truth Values of Compound Statements using ‘And’
4. When two statements are combined using ‘and’, a true compound statement is obtained only if both statements are true.
5. If one or both statements are false, then the compound statement is false.
The truth table:
Let p = statement 1 and q = statement 2.
The truth values for ‘p’ and ‘q’ are as follows:
Example 5:
Determine the truth value of the following statements.
(a) 12 × (–3) = –36 and 15 – 7 = 8.
(b) 5 > 3 and –4 < –5.
(c) Hexagons have 5 sides and each of the interior angles is 90o.
Solution:
(a)
12 × (–3) = –36 ← (p is true)
15 – 7 = 8 ← (q is true)
Therefore 12 × (–3) = –36 and 15 – 7 = 8 is a true statement. (‘p and q’ is true)
(b)
5 > 3 ← (p is true)
–4 < –5 ← (q is false)
Therefore 5 > 3 and –4 < –5 is a false statement. (‘p and q’ is false)
(c)
Hexagons have 5 sides. ← (p is false)
Each of the interior angles of Hexagon is 90o. ← (q is false)
Therefore Hexagons have 5 sides and each of the interior angles is 90o is a false statement. (‘p and q’ is false)