Question

Let A={a1,a2,a3,a4,a5} and B={b1,b2,b3,b4,b5} where ai's and bi's are school going students . Define a relation from A to B by xRy iff y is a true friend of x . If R={(a1,b1),(a2,b2),(a3,b3),(a4,b4),(a5,b5)} . Prove that R is neither one one nor onto

Answer 1

I think your question is wrong because

because we can see that for every element x in A there is only one element y in B such that R(x)=y.So R is one -one


Similarly for every element in B,there is a preimage in A such that R(y)=x and also it is unique.So R is onto


therefore R is a one one and onto function