Question

Let A be the set of all integers which are 3 more than some perfect square. Here are some examples of such integers are: 4 = 1 + 3, 7 = 4 + 3, 3 = 0 + 3, 28 = 25 + 3, Write out the set A as succinctly as you can, using the set-builder notation.

Answer 1

`A = \x`

Explanation:

Required

Represent set A using set-builder notation

First, we need to understand the general rule:

`0^2 + 3 = 0 + 3 = 3`

`1^2 + 3 = 1 + 3 = 4`

`2^2 + 3 = 4 + 3 = 7`

`5^2 + 3= 25 + 3 = 28`

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In general, we can write it as:

`n^2 + 3`

Next, is to determine the values of n;

Since
`n^2` is a perfect square of
`n`, then, the values of n is 0,1,2,3,.....

Hence; Set A can be represented as:
`A = \x`