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:

\frac{x}{a} + \frac{y}{b} = 1 if and only if b x + a y = a b .

(c) It is given that the interior angle of a regular polygon of n sides
is

(1 - \frac{2}{n}) \times 180^{\circ}

.
Make one conclusion by deduction on the size of the interior angle of a regular hexagon.

Solution:
(a)(i) True
(a)(ii) False

(b)

\begin{array}{l} Implication 1: \underline{If \frac{x}{a} + \frac{y}{b} = 1, then b x + a y = a b .} \\ Implication 2: \underline{If b x + a y = a b, then \frac{x}{a} + \frac{y}{b} = 1.} \end{array}

(c)

\begin{array}{l} Size of an interior angle of a regular hexagon \\ = (1 - \frac{2}{6}) \times 180^{\circ} \\ = \frac{2}{3} \times 180^{\circ} \\ = 120^{\circ} \end{array}

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