Function types and bijections – UGC NET Question

Statements A and B give the standard definitions of injective and surjective functions. Statement C is also correct because a bijection is precisely a function that is both one–one and onto. Statement D is false as there are surjective functions that are not injective when the codomain is smaller than the domain. Statement E is false because the definition of a function requires exactly one output in B for each input in A. Hence, A, B and C only are correct, which matches option C.

Option A:
Option A is incomplete since it omits C and thereby fails to mention bijection, which combines the properties described in A and B and is often tested in NET.

Option B:
Option B is incorrect as it adds D, which wrongly claims that surjectivity implies injectivity, so it contains an incorrect statement along with true ones.

Option C:
Option C is correct because it precisely gathers the three accurate definitions and excludes D and E, which misrepresent either implications between properties or the basic definition of a function.

Option D:
Option D is wrong since it includes E, which permits multiple outputs per input, contradicting the concept of a function, and omits A, so it removes a key correct statement and accepts a false one.