Question

Write the set builder form for B = {2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048}
1. {x : x = 2n ^{+ 1} , n ∈ N and 1 ≤ n ≤ 11}
2. {x : x = 2n , n ∈ N and 0 ≤ n ≤ 11}
3. {x : x = 2n , n ∈ N and 1 ≤ n ≤ 11}
4. {x : x = 2n , n ∈ N and 1 ≤ n ≤ 10}

Answer 1

Correct Answer - Option 3 : {x : x = 2n , n ∈ N and 1 ≤ n ≤ 11}

Concept:

Tabular form / Roaster form:

In this method, a set is described by listing all the elements, separated by commas, within the braces {}.

Example: A = {2, 3, 5} is a set of first three prime numbers.

Set –builder form:

In this method, all the elements of the set possess a single common property, which is being enlisted.

Example: B = {x : 6 ≤ x ∈ N ≤ 12}

Calculation:

Given: B = {2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048}

As we can see that, all elements mutilply by 2 with previous elements

So, the required set-builder form of set B = {x : x = 2ⁿ , n ∈ N and 1 ≤ n ≤ 11}