To determine the number of elements in the set
(A×B)∩(B×A), we first need to understand what each component represents.
Let's start by identifying
A×B and
B×A. The Cartesian product
A×B is the set of all ordered pairs where the first element is from
A and the second element is from
B. Similarly,
B×A is the set of all ordered pairs where the first element is from
B and the second element is from
A.
For the given sets:
‌A={1,2,3,4,5}‌B={2,3,6,7} The Cartesian product
A×B is:
A×B={(1,2),(1,3),(1,6),(1,7),(2,2),(2,3),(2,6),(2,7),(3,2),(3,3),(3,6),(3,7),(4,2),(4,3),(4,6),(4,7),(5,2),(5,3),(5,6),(5,7)}
Similarly, the Cartesian product
B×A is:
B×A={(2,1),(2,2),(2,3),(2,4),(2,5),(3,1),(3,2),(3,3),(3,4),(3,5),(6,1),(6,2),(6,3),(6,4),(6,5),(7,1),(7,2),(7,3),(7,4),(7,5)}
The intersection
(A×B)∩(B×A) consists of the ordered pairs present in both
A×B and
B×A. Let's identify these pairs:
Pairs in both
A×B and
B×A are:
{(2,2),(2,3),(3,2),(3,3)}So, the number of elements in
(A×B)∩(B×A) is:
|(A×B)∩(B×A)|=4Therefore, the correct option is Option C: 4 .