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A. A relation RR on a set AA is called an equivalence relation, if it is reflexive, symmetric and transitive.

B. The function f:R→Rf : R \to R defined by f(x)=exf(x) = e^x is not one-one.

C. The one-one function is also known as injective function.

D. The onto function is also known as subjective function.

E. A function f:X→Yf : X \to Y is said to be many-one, if two or more than two elements in set XX have the different image in set YY.

Choose the correct answer from the option given below:

Solution

✅ Correct Option: 1

A is correct (definition of equivalence relation). B is incorrect: f(x)=exf(x) = e^x is one-one since f′(x)=ex>0f'(x) = e^x > 0. C is correct (injective = one-one). D is treated as correct (intended meaning: surjective = onto). E is incorrect: many-one means two elements have the same image, not different images. So A, C, D only.

Note: Option D uses 'subjective' which is taken as the intended term 'surjective'.

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