Sets and functions

[Sk.]

Let S be a set with n elements, n ≥ 3 . Let B be the set of bijective mappings of S
onto itself.
i) Check whether ) ( ,B o is a group or not.
ii) Give the cardinality of the set B .
iii) Is o commutative? Give reasons for you answer

 

[pka]

Let S be a set with n elements, n ≥ 3 . Let B be the set of bijective mappings of S onto itself.
i) Check whether ) ( ,B o is a group or not.
ii) Give the cardinality of the set B .
iii) Is o commutative? Give reasons for you answer

Did you read the posting guidelines? Seeing what you have tried helps us help you.
If \(\displaystyle n=3\) then there are \(\displaystyle 3!=6\) bijections of \(\displaystyle S\leftrightarrow S\).
Now explain that answer. Show your work. And generalize my answer.

 

[Dr.Peterson]

Let S be a set with n elements, n ≥ 3 . Let B be the set of bijective mappings of S
onto itself.
i) Check whether ) ( ,B o is a group or not.
ii) Give the cardinality of the set B .
iii) Is o commutative? Give reasons for you answer

It will help if you explain your notation. I assume "o" is supposed to represent the composition operator, "∘". What do you mean by ") ("? I would have expected you to ask about (B, ∘) being a group.