Question

CK
Let A = {1, 2, 3, 4} and B = {a,b,c}.
1. Which of the following are
relations from A to B?
(i) {(1, b), (1, c), (3, a), (4, b) }
(ii) {(1, a), (b, 4), (C, 3) }
(iii) {(1, a), (a, 1), (2, b), (b, 2)​

Answer 1

Answer:

A X B = {1,2,3,4} X {a,b,c}

         ={(1,a),(1,b),(1,c),(2,a),(2,b),(2,c),(3,a),(3,b),(3,c),(4,a),(4,b),(4,c)}

(i) {(1,b),(1,c),(3,a),(4,b)}

           (1,b),(1,c),(3,a),(4,b) ∈ A X B

           Therefore, it is relation rom A to B.

(ii){(1,a),(b,4),(c,3)}

             (b,4),(c,3) ∉ A X B

             Therefore, it is not a relation from A to B.

(iii){(1,a),(a,1),(2,b),(b,2)}

             (1,a),(2,b) ∉ A X B

             Therefore, it is not a relation from A to B.