JNU SSS 2012 Question 65: Sets, relations and functions
A relation f from set X to set Z is a function if and only if for every element x in X there is a unique element z in Z such that x and z are associated through f. X is called the domain of f and Z the codomain of f. The range of f is the set of all elements in the codomain which are associated with at least one element in the domain.
f is a surjective function if and only if every element in the codomain has an association in the domain. f is an injective function if and only if no two distinct elements in the domain are associated with the same element in the codomain.
Consider the following statements :
(i) There exists an element x in the domain of f such that no element in the codomain is associated with it.
(ii) There exists an element x in the domain of f and two distinct elements z and w in the codomain of f such that both z and w are associated with x.
Which of the following is true?
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A relation f from set X to set Z is a function if and only if for every element x in X there is a unique element z in Z such that x and z are associated through f. X is called the domain of f and Z the codomain of f. The range of f is the set of all elements in the codomain which are associated with at least one element in the domain. f is a surjective function if and only if every element in the codomain has an association in the domain. f is an injective function if and only if no two distinct elements in the domain are associated with the same element in the codomain. Consider the following statements: (i) There exists an element x in the domain of f such that no element in the codomain is associated with it. (ii) There exists an element x in the domain of f and two distinct elements z and w in the codomain of f such that both z and w are associated with x. Which of the following is true? (A) Demonstration of (i) is sufficient to prove that f is not a function but demonstration of (ii) is not sufficient to prove that f is not a function (B) Demonstration of (ii) is sufficient to prove that f is not a function but demonstration of (i) is not sufficient to prove that f is not a function (C) Demonstration of (i) and (ii) is sufficient to prove that f is not a function (D) None of the above
Sets, relations and functions has come up 65 times in 6 exams since 2004.
What this question tests
This question is on Functions: domain, range and composition, part of Sets, relations and functions in Mathematics.
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