Question

if a set has 128 subsets how many elements are there in the set?

Answer 1

If a set has 128 subsets then there are 7 elements in the set

Given :

A set has 128 subsets

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 the number of subsets of the set is 2ⁿ

So by the given condition

$\sf {2}^{n} = 128$

Step 2 of 2 :

Find the number of elements in the set

$\sf {2}^{n} = 128$

$\sf \implies {2}^{n} = {2}^{7}$

$\sf \implies n = 7$

Hence the number of elements in the set is 7

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2. If n(A) = 300, n(A∪B) = 500, n(A∩B) = 50 and n(B′) = 350, find n(B) and n(U).

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Answer 2

Answer:

If a set has $128$ subsets total, then that set has $7$ elements.

Step-by-step explanation:

Given:

A set has $128$ subsets.

To find:

The total elements of a set.

Step 1

The total number of subsets of a set with n components is $2^n.$

The subsets of {1} are the two sets: null set, {1}

The subsets of {1,2} are the four sets: null set, {1}, {2}, {1,2}.

The subsets of {1,2,3} are the eight sets: null set, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}.

Step 2

The set {1,2,3,4} contains a total of $16$ subsets.

The set {1,2,3,4,5} contains a total of $32$ subsets.

The set {1,2,3,4,5,6} contains a total of $64$ subsets.

The set {1,2,3,4,5,6,7} contains a total of $128$ subsets.

If a set has $128$ subsets total, then that set has $7$ components.

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