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#1 2012-05-03 06:30:15

juantheron
Member
Registered: 2011-10-19
Posts: 312

cardanility

Let S={1,2,3,..........n}.If x denotes the set of all subsets of S containing exactly two elements  having 1 as least element,then what is the cardinality of X

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#2 2012-05-03 06:38:02

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: cardanility

Hi juan

For each element we have 2 possibilities:
It goes into a certain subset
or
It doesn't

We then have 2 possibilities for each of the n elements,so tge total number of subsets is 2^n,but we subtract the empty set from the set of subsets to get the answer of 2^n-1


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#3 2012-05-03 06:54:39

juantheron
Member
Registered: 2011-10-19
Posts: 312

Re: cardanility

Thanks anonimnystefy

would you like to explain me the meaning of cardanility

Thanks

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#4 2012-05-03 06:56:55

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: cardanility

Cardinality of a set is the number of its different elements.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#5 2012-05-03 07:25:29

juantheron
Member
Registered: 2011-10-19
Posts: 312

Re: cardanility

Thanks anonimnystefy

got it

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#6 2012-05-03 07:26:36

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: cardanility

You are welcome.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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