Let `A={3,\ 5,\ 7}` , `B={2,\ 6,\ 10}` and `R` be a relation from `A` to `B` defined by `R={(x ,\ y): x` and `y` are relatively prime.} Then, write `R` and `R^(-1)` .

Answer

`R={(3,2),(3,10),(5,2),(5,6),(7,2),(7,6),(7,10)}`

`R^{-1}={(2,3),(10,3),(2,5),(6,5),(2,7),(6,7),(10,7)}`

Explanation

Now, R is defined from A to B, where A is domain/ input set

And B is codomain/output set



So` R^(-1) `can be simply defined as B to A

Where roles of A and B are replaced from input to output and vice-versa.

Most simple method for finding R is by checking each pair.



Say for` gcd(3,2)=1`

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