**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)**

**2**

^{3}= 8 or ⅓ = 1.33.

**(ii)**

**– 6 > – 8 and 6 > 8.**

**(b)**Write down two implications based on the following statement:

$$\overline{)\frac{x}{a}+\frac{y}{b}=1\text{if and only if}bx+ay=ab.}$$

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

*n*sides

*is $\left(1-\frac{2}{n}\right)\times {180}^{\circ}$ .*

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

regular hexagon.

Solution:Solution:

(a)(i)

**True**

**(a)(ii)**

**False**

**(b)**

$$\begin{array}{l}\text{Implication 1:}\underset{\_}{\text{If}\frac{x}{a}+\frac{y}{b}=1,\text{then}bx+ay=ab.}\\ \text{Implication 2:}\underset{\_}{\text{If}bx+ay=ab,\text{then}\frac{x}{a}+\frac{y}{b}=1.}\end{array}$$

**(c)**

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