Question:
Let A = {a, b}. List all relation on A and find their number
Solution:
Any relation on A is a subset of A×A.
$A \times A=\{(a, a),(a, b),(b, a),(b, b)\}$
The subsets are.
{} empty set
$\{(a, a)\}$
$\{(a, b)\}$
$\{(a, a),(a, b)\}$
$\{(b, a)\}$
$\{(b, b)\}$
$\{(b, a),(b, b)\}$
$\{(a, a),(b, a)\}$
$\{(a, b),(b, a)\}$
$\{(a, a),(b, a),(b, b)\}$
$\{(a, a),(b, b)\}$
$\{(a, a),(a, b),(b, a)\}$
$\{(a, a),(a, b),(b, b)\}$
$\{(a, b),(b, a),(b, b)\}$
$\{(a, a),(a, b),(b, a),(b, b)\}$
Thus, there are 16 total relations.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.