Question:
Let $A=\{2,3\}$ and $B=\{3,5\}$
(i) Find $(A \times B)$ and $n(A \times B)$.
(ii) How many relations can be defined from $A$ to $B$ ?
Solution:
Given: A = {2, 3} and B= {3, 5}
(i) $(A \times B)=\{(2,3),(2,5),(3,3),(3,5)\}$
Therefore, n(A × B) = 4
(ii) No. of relation from $A$ to $B$ is a subset of Cartesian product of $(A \times B)$.
Here no. of elements in A = 2 and no. of elements in B = 2.
So, (A × B) = 2 × 2 = 4
So, the total number of relations can be defined from A to B is
$=2^{4}=16$
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.