If (1, 3), (2, 5) and (3, 3) are Three Elements of A × B and n(A × B)=6, Find the Remaining Elements
Question
If \( (1,3) \), \( (2,5) \) and \( (3,3) \) are three elements of \( A \times B \) and \( n(A \times B)=6 \), then the remaining three elements are ……………………….
Solution
Given ordered pairs:
\[ (1,3),\ (2,5),\ (3,3) \]
From these pairs:
\[ A=\{1,2,3\} \]
and
\[ B=\{3,5\} \]
Now,
\[ A \times B = \{(a,b): a\in A,\ b\in B\} \]
So all possible ordered pairs are:
\[ A \times B= \{ (1,3), (1,5), (2,3), (2,5), (3,3), (3,5) \} \]
Three elements are already given:
\[ (1,3),\ (2,5),\ (3,3) \]
Therefore, the remaining three elements are:
\[ \boxed{(1,5),\ (2,3),\ (3,5)} \]