10th Maths Example 1.4 Answer
Let A = {3, 4, 7, 8} and B = {1, 7, 10}. Which of
the following sets are relations from A to B ?
(i) R₁= {(3, 7), (4, 7), (7, 10), (8, 1)}
(ii) R₂= {(3, 1), (4, 12)}
(iii) R₃= {(3, 7), (4, 10), (7, 7), (7, 8), (8, 11), (8, 7), (8, 10)}
Solution :
A×B = {(3, 1), (3, 7), (3, 10), (4, 1), (4, 7),
(4,10), (7,1), (7,7), (7,10), (8, 1), (8, 7), (8, 10)}
(i) We note that R₁ ⊆ A × B. Thus, R₁
is a relation from A to B.
(ii) Here, (4, 12) ∈ R₂, but (4, 12) ∉ A × B. So, R₂
is not a relation from A to B.
(iii) Here, (7, 8) ∈ R₃, but (7, 8) ∉ A × B. So R₃ is not a relation from A to B.