A set has 256 subsets how many element has the set?
for n elements, the number of subsets = 2^n
2^n = 256
we know 2^8 = 256
So there are 8 elements
8 Elements
We use 2^n= to the number of subset
2ⁿ=256
2ⁿ=2⁸
n=8
:. Number of elements in set A are 8
Can you generalize the relationship between the number of elements in a set and
the number of subsets?
We use 2^n= to the number of subset
2ⁿ=256
2ⁿ=2⁸
n=8
:. Number of elements in a set are 8
No. of subsets = 2^n
256 = 2^n
2×2×2×2×2×2×2×2 = 2^n
2^8 = 2^n
8 = n
n = 8
.: There are 8 elements.
As 2^n=256
2^n=2^8
simplifying the base 2, get
n=8 as n is the number of elements in a set, there are 8 elements in a set
To find out the number of elements in a set, given the number of subsets it has, you can use a formula.
Let's say the original set has n elements. The number of subsets can be determined using the formula 2^n, where '^' denotes exponentiation.
In this case, we are given that the set has 256 subsets. So we can set up the equation:
2^n = 256
To solve for n, we can rewrite 256 as a power of 2: 256 = 2^8
So 2^n = 2^8
For the equation to hold true, the exponents must be equal:
n = 8
Therefore, the original set has 8 elements.
Solution :n(subset of A)=2n
n=? 256=2n
First we find prime factorization of 256. 2n=256
2n=2 The power of 8
n=8
Therefore the number of elements of set are 8