3.7.3 Logical Reasoning, SPM Paper 2 (Long Questions)

Question 6:
(a) Complete the following mathematical sentence by writing the symbol > or <.

(b) Complete the conclusion in the following argument:
$$\boxed{\begin{array}{l}\text{ Premise 1 : If }{n}^{\frac{1}{2}}=\sqrt{n},\text{ then }{4}^{\frac{1}{2}}=\sqrt{4}=2.\\ \text{ Premise 2 : }{n}^{\frac{1}{2}}=\sqrt{n}\\ \text{ Conclusion : \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}\end{array}}$$
(c) Make a general conclusion by induction for the sequence of numbers 10, 35, 70, … which follows the following pattern.


Solution:
(a)(i) 5³   <    20 is a false statement.
(a)(ii)   – 3    >    – 10 is a true statement.

(b)
$\text{Conclusion :}{4}^{\frac{1}{2}}=\sqrt{4}=2$

(c) 5 (n + 1)² – 10, where n = 1, 2, 3, …

Question 7:
(a)(i) State whether the following compound statement is true or false.

3 + 3 = 9 or   3 × 3 = 9

(a)(ii) Determine whether the following converse is true or false.

If x > 3, then x > 7

(b) Write down Premise 2 to complete the following argument:
Premise 1: If y = mx + 5 is a linear equation, then m is a gradient of the straight line.
Premise 2: _____________________
Conclusion: 2 is the gradient of the straight line.

(c) Angle subtended at the centre of a regular polygon with n sides is $\frac{{360}^o}{n}.$
Make one conclusion by deduction for the angle subtended at the centre of a regular polygon with 5 sides.

Solution:
(a)(i) True

(a)(ii) The converse is true

(b) Premise 2: y = 2x + 5 is a linear equation

(c)
$\begin{array}{l}\text{Angle subtended at the centre of a regular pentagon}\\ =\frac{{360}^o}{n}\\ =\frac{{360}^o}{5}\\ ={72}^o\end{array}$