MATHS 3 Marks Question

1. By the definition of equality of ordered pairs,

$\Big(\frac{\text{a}}{3}+1,\text{b}-\frac{2}{3}\Big)=\Big(\frac{5}{3},\frac{1}{3}\Big)$

$\Rightarrow\frac{\text{a}}{3}+1=\frac{5}{3}$ and $\text{b}-\frac{2}{3}=\frac{1}{3}$

$\Rightarrow\frac{\text{a}}{3}=\frac{5}{3}=-1$ and $\text{b}=\frac{1}{3}+\frac{2}{3}$

$\Rightarrow\frac{\text{a}}{3}=\frac{5-3}{3}$ and $\text{b}=\frac{1+2}{3}$

$\Rightarrow\frac{\text{a}}{3}=\frac{2}{3}$ and $\text{b}=\frac{3}{3}$

$\Rightarrow\text{a}=2$ and $\text{b}=1$

2. By the definition of equality of ordered pairs,

(x + 1, 1) = (3, y - 2)

⇒ x + 1 = 3 and 1 = y - 2

⇒ x = 3 - 1 and x + 2 = y

⇒ x = 2 and 3 = y

⇒ x = 2 and y = 3

1. Set builder form of the relation from P to Q is,

$\text{R}=\{(\text{x, y}):\text{y}=\text{x}-2,\text{x}\in\text{P},\text{y}\in\text{Q}\}$

2. Roster form of the relation from P to Q is,

R = {(5, 3), (6, 4), (7, 5)}

Domain(R) = {5, 6, 7}

Range(R) = {3, 4, 5}

1. Now, $\frac{\text{a}}{\text{b}}$ stands for 'a divides b'. For the elements of the given sets A and A, we find that,

 $\frac{1}{1},\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6},\frac{2}{2},\frac{2}{4},\frac{2}{6},\frac{3}{3},\frac{3}{6},\frac{4}{4},\frac{5}{5},\frac{6}{6}$

$\therefore$ Relation R in roster form is

R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (5, 5), (6, 6)}

2. Domain(R) = {1, 2, 3, 4, 5, 6}
3. Range(R) = {1, 2, 3, 4, 5, 6}