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

injective (one- one ) and surjective (into)

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injective (one- one ) and not surjective (into)

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not injective (one- one ) and surjective (into)

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not injective (one- one ) and not surjective (into)

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Solution

The correct option is D not injective (one- one ) and surjective (into)
We have {(x, y) : x is a person, y is the mother of x}. Clearly each person 'x' has only one biological mother. So above set of ordered pair is a function. Now more than one person may have same mother. So function is many-one and surjective.

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Similar questions

Q. Are the following sets of ordered pairs functions? If so, examine wheather the mapping is surjective or injective.
(a) {(x,y):x is a person, y is the mother of x}

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

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

Q. 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}

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

(i) $f = {(x, y) : x is a person, y is the mother of x}$

(ii) $g = {(a, b) : a is a person, b is the ancestor of a}$

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

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