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Archangel Macsika

Every function is a relation, but the converse is not true.”--True or false? Justify with an example.

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If we have a function f:X\to Y, then it is also a relation \{(x,f(x):x\in X\}\subset X\times Y. Therefore, each function is a relation. On the other hand, the relation R=\{(1,1),(1,2)\}\subset\{1,2\}\times\{1,2\} is not a function because of for the element 1 there are two element x=1 and y=2 such that (1,x),(1,y)\in R. We conclude that there exist relations that are not functions.


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