Question

if the number of non empty subsets of a set is 4095 then the number of elements of the set is​

Answer 1

Answer:

$\textbf{The number of elements of a given set is 12}$

$\text{option (c) is correct}$

Step-by-step explanation:

$\text{Given:}$

$\text{The number of non empty subset of a set is 4095}$

$\textbf{The number of non-empty of subset of a set having m elements is }\bf\\2^m-1$

$\text{As per given data, we have}$

$2^m-1=4095$

$2^m=4096$

$2^m=2^{12}$

$\implies\,\boxed{\bf\,m=12}$

$\therefore\textbf{The number of elements of a given set is 12}$

Answer 2

The number of elements in the set is 12

Step-by-step explanation:

The number of non empty subset of a set  is 4095

then we know that

The number of non empty subset of a set having the elements is $2^n -1$

therefore

$2^n -1 = 4095 \\\\2^n = 4095+1 \\\\2^n= 4096\\\\2^n = 2^1^2\\\\n= 12$

hence , The number of elements in the set is 12

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