Question

Answer each question. Justify your answer with a brief explanation, including an example where appropriate.

Consider the relation R1 = {(1, 2),(1, 3),(2, 2),(3, 2)} on A = {1, 2, 3}. Is R1 a function?

Answer 1

No, R1 is not a function because the element '1' in set A is associated with two different elements in the co-domain, which violates the definition of a function.

Step-by-step explanation:

To determine if the relation R1 is a function, we need to check if each element in the domain has exactly one corresponding element in the range. If there is any element in the domain that has multiple corresponding elements in the range, then the relation is not a function.

In the given relation R1 = {(1, 2),(1, 3),(2, 2),(3, 2)}, we can see that the element 1 in the domain has two corresponding elements, 2 and 3, in the range. Therefore, R1 is not a function.