Question

If number of proper subsets of a set is 63, then the number of elements in the set is .........​

Answer 1

Answer:

the number of elements in the set is 6

Step-by-step explanation:

If number of proper subsets of a set is 63, then the number of elements in the set is

Let say the number of elements in the set is  = n

number of proper subsets = 2ⁿ - 1

2ⁿ - 1 = 63

=> 2ⁿ = 64

=> 2ⁿ = 2⁶

=> n = 6

the number of elements in the set is 6

Answer 2

The number of elements in the set is "6".

Step-by-step explanation:

We have,

The number of proper subsets of a set = 63

Let the number of elements in the set = n

To find, the number of elements in the set = ?

We know that,

The number of proper subsets $=2^{n} -1$

⇒ $2^{n} -1=63$

⇒$2^{n}=63+1=64$

⇒ $2^{n}=2^{6}$

Equating the power of 2, we get

⇒ n = 6

∴ n = 6

Hence, the number of elements in the set is "6".