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Question
State whether the following relations are functions or not. If it is a function check for one-to-oneness and ontoness. If it is not a function, state why?
If A = {a, b, c} and f = {(a, c), (b, c), (c, b)}; (f : A → A)
Sum
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Solution
A = {a, b, c}
f = {(a, c), (b, c), (c, b)}; f : A → A
f is a function since every element in the domain has a unique image in the codomain.
f is not one-one.
a, b belonging to the domain A has the same image in the codomain A.
f is not onto since belonging to the codomain A does not have preimage in the domain A
Thus the relation / is a function from A to A and it is neither one-one nor onto.
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