Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.
(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}.

Question

Philoid · Accepted Answer

(i){(x, y): x is a person, y is the mother of x}.

Here, (x, y) is an ordered pair which associates each person (x) to his(her) mother (y).

Now, each person will have only one mother so we can say that for each value of x there is an association to a unique value of y.

Hence,(x, y) represent a function.

Also, more than one person may have same mother.

i.e., two or more distinct value of x may have same value of y.

So, (x, y) is many-one function or surjective.

(ii){(a, b): a is a person, b is an ancestor of a}.

Here, (a, b) is an ordered pair which associates each person (a) to his(her) ancestor (b).

Now, any person can have more than one ancestor so we can say that each value of a does not have a unique value of b.

Hence, (a,b) does not represent a function.

Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.(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}.