A. A relation on a set is called an equivalence relation, if it is reflexive, symmetric and transitive.
B. The function defined by 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 is said to be many-one, if two or more than two elements in set have the different image in set .
Choose the correct answer from the option given below:
A. A relation on a set is called an equivalence relation, if it is reflexive, symmetric and transitive.
B. The function defined by 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 is said to be many-one, if two or more than two elements in set have the different image in set .
Choose the correct answer from the option given below:
Solution
A is correct (definition of equivalence relation). B is incorrect: is one-one since . 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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