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Archangel Macsika

Determine whether the following relations are injective and/or subjective function. Find universe of the functions if they exist. A = 1,2,3,4,5 B=1,2,3,4,5 R = (1,2),(2,3),(3,4),(4,5),(5,1)

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Let A = \{1,2,3,4,5\}, B=\{1,2,3,4,5\}.

Let us determine whether the relation R = \{(1,2),(2,3),(3,4),(4,5),(5,1)\} is an injective function. Since there are no different pairs with the same second coordinate, we conclude that the relation is an injective function.

Taking into account that range(R)=\{b\in B\ |\ (a,b)\in R\}=\{2,3,4,5,1\}=B, we conclude that the relation R is a surjective function.

It follows that the inverse of R exists and it is equal to R^{-1}=\{(b,a)\ |\ (a,b)\in R\}=\{(2,1),(3,2),(4,3),(5,4),(1,5)\}.


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Question ID: mtid-5-stid-8-sqid-1544-qpid-1282