Question 908676: Please help me solve this:
1. In how many ways can 5 people be arranged on a bench?around a circular table?
2. If two of them insist on sitting next to each other, how many arrangements are possible?
Give two sets A, B and an application f:A -> B such that:
a) f is bijective,
b) is injective, but not surjective,
c) f is surjective, but not injective,
d) f is neither injective nor surjective.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Please help me solve this:
1. In how many ways can 5 people be arranged on a bench?::: 5! = 120
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around a circular table?:: 4! = 24
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2. If two of them insist on sitting next to each other, how many arrangements are possible?
Arrangements of the special 2:: 2 ways
Arrangements of the 5 where 2 act as a unit: 4!
Ans 4!*2 = 24*2 = 48 arrangements
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Give two sets A, B and an application f:A -> B such that:
Use Google to see examples.
Search for "bijective function".
a) f is bijective,
b) is injective, but not surjective,
c) f is surjective, but not injective,
d) f is neither injective nor surjective.
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Cheers,
Stan H.
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