4.3 Operations on Statements (Sample Questions)


Example 1:
Form a compound statement by combining two given statements using the word ‘and’.
(a) × 12 = 36
 7 × 5 = 35
(b) 5 is a prime number.
 5 is an odd number.
(c) Rectangles have 4 sides.
 Rectangles have 4 vertices.

Solution:

(a) × 12 = 36 and 7 × 5 = 35
(b) 5 is a prime number and an odd number.
(c) Rectangles have 4 sides and 4 vertices.



Example 2:
Form a compound statement by combining two given statements using the word ‘or’.
(a) 16 is a perfect square. 16 is an even number.
(b) 4 > 3.  -5 < -1

Solution:
(a) 16 is a perfect square or an even number.
(b) 4 > 3 or -5 < -1.



Example 3:
Determine whether each of the following statements is true or false.
(a) × (-4) = -12 and 13 + 6 = 19
(b) 100 × 0.7 = 70 and 12 + (-30) = 18

Solution:
When two statements are combined using ‘and’, a true compound statement is obtained only if bothstatements are true.
If one or bothstatements are false, then the compound statement is false.

(a)
Both the statements ‘3 × (-4) = -12’ and ‘13 + 6 = 19’ are true. Therefore, the statement ‘3 × (-4) = -12 and 13 + 6 = 19’ is true.

(b)
The statement ‘12 + (-30) = 18’ is false. Therefore, the statement ‘100 × 0.7 = 70 and 12 + (-30) = 18’ is false.



Example 4:
Determine whether each of the following statements is true or false.
(a) m + m = m2or p × p × p = p3
(b)  64 3 = 4 or 27 3 = 3

Solution:
When two statements are combined using ‘or’, a false compound statement is obtained only if bothstatements are false.
If one or bothstatements are true, then the compound statement is true.

(a) Both the statements ‘m+ m = m2’ and ‘p × p × p= p3’ are false. Therefore the statement m + m = m2or p × p × p = p3 is false.

(b) The statement  27 3 = 3  is true. Therefore, the statement  64 3 = 4 or 27 3 = 3  is true.

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