Representation of a Relation A relation can be represented algebr… - Vidyadip

Question

Representation of a Relation
A relation can be represented algebraically by roster form or by set-builder form and visually it can be represented by an arrow diagram which are given below
i. Roster form In this form, we represent the relation by the set of all ordered pairs belongs to R.
ii. Set-builder form In this form, we represent the relation $R$ from set $A$ to set $B$ as $R=\{(a, b)$ : $a \in A, b \in B$ and the rule which relate the elements of A and B ).
iii. Arrow diagram To represent a relation by an arrow diagram, we draw arrows from first element to second element of all ordered pairs belonging to relation R.
Questions:
i. If n(A) = 3 and B = {2, 3, 4, 6, 7, 8} then find the number of relations from A to B. (1)
ii. If A = {a, b} and B = {2, 3}, then find the number of relations from A to B. (1)
iii. If A = {a, b} and B = {2, 3}, write the relation in set-builder form. (2)
OR
Express of R = {(a, b): 2a + b = 5; a, b ∈ W} as the set of ordered pairs (in roster form). (2)

✓

Answer

i. Number of relations $=2^{ mn }$
$=2^{3 \times 6}=2^{18}$
ii. Number of relations $=2^{ mn }$
$=2^{2 \times 2}=2^4=16$
iii. $R=\{(x, y): x \in P, y \in Q$ and $x$ is the square of $y\}$
|OR
Here, W denotes the set of whole numbers.
We have $2 a + b =5$ where $a , b \in W$
$\therefore a=0 \Rightarrow b=5$
$\Rightarrow a=1 \Rightarrow b=5-2=3$
and $a =2 \Rightarrow b=1$
For a > 3, the values of b given by the above relation are not whole numbers.
$\therefore A =\{(0,5),(1,3),(2,1)\}$

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