Question

if a set p has 510 non empty proper subset then find the cardinal number​

Answer 1

given nonempty proper subsets =510

total sunsets = 510+ empty set + the set itself

= 512

2^n=512 =2^9

2^n =2^9

the cardinal number =n =9

Answer 2

Answer:

The cardinal number is 9

Given no. of non empty proper subset is $510$.

We have to find the cardinal number​.

By total subsets: No. of proper subsets $+$ No. of improper subsets

$= 510 + ( empty\: set + the\: set\: itself)$

$= 510 + 2 = 512$.  -------(1)

A set contains = n elements

Total no. Of subsets = Power of $2$ is $n$

Power of $2$ is n $= 512 =$ Power of $2$ is $9$.    _______ ( from 1)

Power of $2$ is $n$ $=$ Power of $2$ is $9$

$n = 9$

Hence the cardinal number is $9$ .

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