NCERT Class XI Mathematics - Relations and Functions - Solutions
© examsnet.com
Question : 34
Total: 36
Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true?
(i) f is a relation from A to B.
(ii) f is a function from A to B.
Justify your answer in each case.
(i) f is a relation from A to B.
(ii) f is a function from A to B.
Justify your answer in each case.
Solution:
Given A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16}
f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}.
(i) True
Since f ⊂ A × B. Thus, f is a relation from A to B.
(Since Each element of f is an element of A × B)
(ii) False
Since (2, 9), (2, 11) ∈ f i.e., f contains two ordered pairs with the same first element.
Hence, f is not a function from A to B.
f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}.
(i) True
Since f ⊂ A × B. Thus, f is a relation from A to B.
(Since Each element of f is an element of A × B)
(ii) False
Since (2, 9), (2, 11) ∈ f i.e., f contains two ordered pairs with the same first element.
Hence, f is not a function from A to B.
© examsnet.com
Go to Question: