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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): x is a person, y is the mother of x}. (ii){(a, b): a is a person, b is an ancestor of a}. 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
8 months ago
Dear Student

(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.
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.
Thanks

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