In a school at Chandigarh, students of class XI were discussing about the relations and functions. ThreeStudents Ankita, Babita and Kavita form three sets A={1,2,3,4,5},B={2,4,6} and K={5,7}(i) Find n(A×B) and n(K×B)(ii) A correspondence of elements from A to B given as {(1,2),(2,2),(3,4),(3,6),(4,4), (5,6)}.(iii) If the function f:B→K such that (b, k)∈f and b<k, defined by f={(1,5),(x,5),(5, y),(2,7),(4,7)}, then find x and y.
Question
In a school at Chandigarh, students of class XI were discussing about the relations and functions. ThreeStudents Ankita, Babita and Kavita form three sets A={1,2,3,4,5},B={2,4,6} and K={5,7}(i) Find n(A×B) and n(K×B)(ii) A correspondence of elements from A to B given as {(1,2),(2,2),(3,4),(3,6),(4,4), (5,6)}.(iii) If the function f:B→K such that (b, k)∈f and b<k, defined by f={(1,5),(x,5),(5, y),(2,7),(4,7)}, then find x and y.
Solution
(i) To find n(A×B), we need to determine the number of elements in the Cartesian product of sets A and B. The Cartesian product A×B is formed by taking each element from set A and pairing it with each element from set B.
In this case, A={1,2,3,4,5} and B={2,4,6}. So, the Cartesian product A×B would be {(1,2),(1,4),(1,6),(2,2),(2,4),(2,6),(3,2),(3,4),(3,6),(4,2),(4,4),(4,6),(5,2),(5,4),(5,6)}.
Therefore, n(A×B) = 15.
Similarly, to find n(K×B), we need to determine the number of elements in the Cartesian product of sets K and B. The Cartesian product K×B is formed by taking each element from set K and pairing it with each element from set B.
In this case, K={5,7} and B={2,4,6}. So, the Cartesian product K×B would be {(5,2),(5,4),(5,6),(7,2),(7,4),(7,6)}.
Therefore, n(K×B) = 6.
(ii) The correspondence of elements from A to B is given as {(1,2),(2,2),(3,4),(3,6),(4,4),(5,6)}. This means that each element from set A is paired with a corresponding element from set B.
(iii) The function f:B→K is defined as f={(1,5),(x,5),(5,y),(2,7),(4,7)}. We need to find the values of x and y.
From the given function, we can see that (1,5) and (5,y) are already defined. So, x=2 and y=7.
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