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4.3 Operations on Statements

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4.3 Operations on Statements (Part 1)
 
(A) Nagating a Statement using ‘No’ or ‘Not’
 
1. Negation of a statement refers to changing the truth value of the statement, that is, changing a true statement to a false statement and vice versa, using the word ‘not’ or ‘no’.
 
Example 1:
Change the true value of the following statements by using ‘no’ or ‘not’.
(a) 17 is a prime number.
(b) 39 is a multiple of 9.
 
Solution:
(a) 17 is not a prime number. (True to false)
(b) 39 not is a multiple of 9. (False to true)


2. A compound statement can be formed by combining two given statements using the word ‘and’.
 
Example 2:
Identify two statements from each of the following compound statements.
(a) All pentagons have 5 sides and 5 vertices.
(b) 33 = 27 and 43 = 64
 
Solution:
(a) All pentagons have 5 sides.
 All pentagons have 5 vertices.
(b) 33 = 27
  43 = 64



Example 3:
Form a compound statement from each of the following pairs of statements using the word ‘and’.
(a) 19 is a prime number.
  19 is an odd number.
(b) 15 – 5 = 10
  15 × 5 = 75

Solution:
(a) 19 is a prime number and an odd number. ← (Repeated words can be eliminated when combining two statements using ‘and’.)

(b) 15 – 5 = 10 and15 × 5 = 75.


3. A compound statement can also be formed by combining two given statements using the word ‘or’.
 
Example 4:
Form a compound statement from each of the following pairs of statements using the word ‘or’.
(a) 11 is an odd number.
  11 is a prime number.
(b) − 3 = − 27 3 − 3 = − 4 + 1

Solution:
(a) 11 is an odd number or a prime number.
( b) − 3 = − 27 3 or − 3 = − 4 + 1