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  • 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 \} .\\

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

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

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

Answers (1)


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

Therefore, each person (x) has only one biological mother.

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

Therefore, there are more than one person who may have the same mother. Hence, the function is many-one and surjective.

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

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

Therefore, it is not a function.

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