Question

If the number of proper subsets of a set is 511.Then the number of elements of set is​

Answer 1

Answer:

9

Step-by-step explanation:

$2^{n}$ - 1 = 511

$2^{n}$ = 511 +1

$2^{n}$ = 512

$2^{n}$ = $2^{9}$

n = 9

Answer 2

The number of elements in the set is 9

Given :

The number of proper subsets of a set is 511

To find :

The number of elements in the set

Solution :

Step 1 of 2 :

Form the equation to find the number of elements in the set

Let the number of elements in the set = n

We know that if a set contains n elements then number of proper subsets of the set is (2ⁿ - 1)

So by the given condition

$\sf {2}^{n} - 1 = 511$

Step 2 of 2 :

Find the number of elements in the set

$\sf {2}^{n} - 1 = 511$

$\sf \implies {2}^{n} = 511 + 1$

$\sf \implies {2}^{n} = 512$

$\sf \implies {2}^{n} = {2}^{9}$

$\sf \implies n = 9$

Hence the number of elements in the set is 9

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