Question 3:
(a) Complete each of the following statements with the quantifier ‘all’ or ‘some’ so that it will become a true statement.
(i) ___________ of the prime numbers are odd numbers.
(ii) ___________ pentagons have five sides.
(b) Write down two implications based on the following statement:
(c) Complete the premise in the following argument:
Solution:
(a)(i) Some of the prime numbers are odd numbers.
(a)(ii) All pentagons have five sides.
(b) Implication 1: If A ∩ B = B, then A υ B = A.
Implication 2: If A υ B = A, then A ∩ B = B.
(c) Conclusion: 12 is a factor of 48.
(a) Complete each of the following statements with the quantifier ‘all’ or ‘some’ so that it will become a true statement.
(i) ___________ of the prime numbers are odd numbers.
(ii) ___________ pentagons have five sides.
(b) Write down two implications based on the following statement:
A ∩ B = B if and only if A υ B = A. |
Premise 1: If a number is a factor of 24, then it is a factor of 48.
Premise 2: 12 is a factor of 24.
Conclusion: _____________________
|
Solution:
(a)(i) Some of the prime numbers are odd numbers.
(a)(ii) All pentagons have five sides.
(b) Implication 1: If A ∩ B = B, then A υ B = A.
Implication 2: If A υ B = A, then A ∩ B = B.
(c) Conclusion: 12 is a factor of 48.
Question 4:
(a) Combine the following two statements to form one true statement.
Statement 1: (– 3)² = 9
Statement 2: –3 (3) = 19
Solution:
(a) (– 3)² = 9 or –3 (3) = 19.
(b) Premise 1: All multiples of 25 is divisible by 5.
(c) 3 (2)n + n, where n = 1, 2, 3, …
(a) Combine the following two statements to form one true statement.
Statement 1: (– 3)² = 9
Statement 2: –3 (3) = 19
(b) Complete the premise in the following argument:
Premise 1: _____________________
Premise 2: x is a multiple of 25.
Conclusion: x is a divisible of 5. |
(c) Make a general conclusion by induction for the sequence of numbers 7, 14, 27, … which follows the following pattern.
7 = 3 (2)1 + 1
14 = 3 (2)2 + 2
27 = 3 (2)3 + 3
…. = ………..
(a) (– 3)² = 9 or –3 (3) = 19.
(b) Premise 1: All multiples of 25 is divisible by 5.
(c) 3 (2)n + n, where n = 1, 2, 3, …