- Home
- Standard 12
- Mathematics
1.Relation and Function
hard
The minimum number of elements that must be added to the relation $R =\{( a , b ),( b , c )\}$ on the set $\{a, b, c\}$ so that it becomes symmetric and transitive is:
A
$4$
B
$7$
C
$5$
D
$3$
(JEE MAIN-2023)
Solution
For Symmetric $(a, b),(b, c) \in R$
$\Rightarrow(b, a),(c, b) \in R$
For Transitive $(a, b),(b, c) \in R$
$\Rightarrow(a, c) \in R$
Now
$1.$ Symmetric
$\therefore(a, c) \in R \Rightarrow(c, a) \in R$
$2.$ Transitive
$\therefore(a, b),(b, a) \in R$
$\Rightarrow(a, a) \in R \&(b, c),(c, b) \in R$
$\Rightarrow(b, b) \&(c, c) \in R$
$\therefore$ Elements to be added
$\left\{\begin{array}{r}(b, a),(c, b),(a, c),(c, a) \\,(a, a),(b, b),(c, c)\end{array}\right\}$
Number of elements to be added $=7$
Standard 12
Mathematics
Similar Questions
medium