Question

Are the following sets of ordered pairs functions? If so, examine whether the mapping is surjective or injective:
(i) {(x, y) : x is a person, y is the mother of x}
(ii) {(a, b) : a is a person, b is an ancestor of a}

Answer 1

Given: f :{(x,y) : x is a person, y is mother of x}

Let x${}_1$ and x${}_2$ be two persons.

Step 1: Injective or One-one function

f(x${}_1$)=f(x${}_2$) $\Rightarrow$ both x${}_1$ and x${}_2$ have same mother but this does not imply x${}_1$ and x${}_2$ are same x${}_1$ need not be x${}_2$. They can be brother or sister.

Hence, f is not injective.

Step 2: Surjective or Onto function

For every mother defined by (x, y), there exists a person x for whom y is mother.

Therefore, f is a surjective function.