Injective and surjective function facts – UGC NET Question

Statements A, B and C give standard definitions of injective, surjective and bijective functions. E is also correct in the finite equal-cardinality case: an injective map from A to B must be surjective. D is false because surjectivity alone does not guarantee injectivity; many onto but not one-to-one functions exist. Therefore A, B, C and E only are correct.

Option A:
Option A is correct as it aggregates all the true statements about these function types, including the finite-set result, while leaving out D, which wrongly treats surjectivity as forcing injectivity.

Option B:
Option B is incorrect because it omits E, and E is a true theorem for finite sets of equal size (injective ⇒ surjective).

Option C:
Option C is incorrect because it omits A (a true definition of injective), so it does not list all correct statements.

Option D:
Option D is incorrect because it omits B (a true definition of surjective), so it does not list all correct statements.