3.7.2 Logical Reasoning, SPM Paper 2 (Long Questions)


Question 4:
(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
…. = ………..
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, …


Question 5:
(a) State if each of the following statements is true or false.
 (i)    23= 8 or ⅓ = 1.33.
 (ii)  – 6 > – 8 and 6 > 8.
 
(b) Write down two implications based on the following statement:

x a + y b =1 if and only if bx+ay=ab.

(c) It is given that the interior angle of a regular polygon of n sides 
  is   ( 1 2 n ) × 180 .
  Make one conclusion by deduction on the size of the interior angle of a regular hexagon.

Solution:

(a)(i) True
(a)(ii) False

(b) 

Implication 1:   If   x a + y b =1, then bx+ay=ab. _ Implication 2:   If  bx+ay=ab, then  x a + y b =1. _

(c)
Size of an interior angle of a regular hexagon = ( 1 2 6 ) × 180 = 2 3 × 180 = 120

Leave a Comment