Question

{1,3,7,15,..} in set builder form

Answer 1

Answer:

$\bf\{x:\,x=2^n-1,\text{n is a natural number}\}$

Step-by-step explanation:

Set builder form:

In this form, common property posssessed by each element is written inside the curly brackets.

Given:

{1,3,7,15,..}

Consider,

$1=2^1-1$

$3=2^2-1$

$7=2^3-1$

$16=2^4-1$

Now the above set, can be written set builder form as

$\bf\{x:\,x=2^n-1,\text{n is a natural number}\}$

Answer 2

{x:  x = 2n - 1, n ∈ N}

Step-by-step explanation:

{1,3,7,15,..} in set builder form is {x :  x = 2ⁿ - 1, n ∈ N}

In set builder form, the set is written in shorthand.

Here, n is the Natural number.

The set of x is any natural number which is one less than two times the number.

When n = 1;

2ⁿ  - 1 = 2¹  -1 = 2 -1 = 1

When n = 2;

2ⁿ - 1 = 2² -1 = 4 -1 = 3

When n = 3;

2ⁿ - 1 = 2³ -1 = 8 -1 = 7

Learn more:

Write the given set in the set-builder form: {3, 6, 9, 12}

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