If f:$A \to B$ is a bijective function and if n(A) = 5, then n(B) is equal to
(A). 10
(B). 4
(C). 5
(D). 25.
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Hint: Before attempting this question, one should have prior knowledge about the bijective functions and also remember functions which are one-one and onto are bijective functions, use this information to approach the solution of the question.
Complete step-by-step answer:
According to the given information we have a function f:$A \to B$ is a bijective function where n(A) = 5
Before approach towards the solution of the problem let’s discuss about the bijective functions
The functions which are both one-one and onto functions are named bijective functions
Therefore, elements belong to set B is an image of function f
Also, we know that when function is one-one than each element belongs to that function have different image
Which means the numbers of elements belong to set B is equal to the numbers present in set A
Therefore, n(B) is equal to n(B)
So, n(B) = 5 since n(A) = 5
Hence, option C is the correct answer.
Note: In the above solution we came across the term “function” which can be explained as relation between the provided inputs and the outputs of the given inputs such that each input is directly related to the one output. The representation of a function is given by supposing if there is a function “f” that belongs from X to Y then the function is represented by $f:X \to Y$examples of function are one-one functions, onto functions, bijective functions, trigonometric function, binary function, etc.
Complete step-by-step answer:
According to the given information we have a function f:$A \to B$ is a bijective function where n(A) = 5
Before approach towards the solution of the problem let’s discuss about the bijective functions
The functions which are both one-one and onto functions are named bijective functions
Therefore, elements belong to set B is an image of function f
Also, we know that when function is one-one than each element belongs to that function have different image
Which means the numbers of elements belong to set B is equal to the numbers present in set A
Therefore, n(B) is equal to n(B)
So, n(B) = 5 since n(A) = 5
Hence, option C is the correct answer.
Note: In the above solution we came across the term “function” which can be explained as relation between the provided inputs and the outputs of the given inputs such that each input is directly related to the one output. The representation of a function is given by supposing if there is a function “f” that belongs from X to Y then the function is represented by $f:X \to Y$examples of function are one-one functions, onto functions, bijective functions, trigonometric function, binary function, etc.