Math Is Fun Forum

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

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

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“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.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: cardanility

Thanks anonimnystefy

would you like to explain me the meaning of cardanility

Thanks

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.

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“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.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: cardanility

Thanks anonimnystefy

got it

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.