Answer to Question #210478 in Discrete Mathematics for Sach

Question

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

Answer 1

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.

Answer: true