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in Sets, Relations and Functions by (49.1k points)
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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? 

(i) If A = {a, b, c] and /= {(a, c), (b, c), (c, b)};(f: A ➝ A). 

(ii) If X = {x, y, z} and /= {(x, y), (x, z), (z, x)}; (f: X ➝ X).

1 Answer

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Best answer

(i) f : A ➝ A

It is a function but it is not 1 – 1 and not onto function. 

(ii) f : X ➝ X

x ∈ X (Domain) has two images in the co-domain x. It is not a function.

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