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

Answer:

$A = \{x|x\ E\ n^2 + 3, n \geq 0 \}$

Step-by-step 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: $A = \{x|x\ E\ n^2 + 3, n \geq 0 \}$