Are the following set of ordered pairs functions?

Question:

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}.

Solution:

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

It’s clearly seen that each person ‘x’ has only one biological mother.

Hence, the above set of ordered pairs make a function.

Now more than one person may have same mother. Thus, the function is many-many one and surjective.

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

It’s clearly seen that any person ‘a’ has more than one ancestors.

Thus, it does not represent a function.

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