Question

A={red, orange, yellow, green,blue,indigo,violet} write the following set in builder form or rule method.​

Answer 1

Answer:

{x:x is a color of the rainbow}

Answer 2

Answer:

The given set in set builder form is $A = \{x | x~\mbox{ is ~a ~color~ in~ rainbow}\}$

Step-by-step explanation:

Given a set of elements,

$A=\{\mbox{red, orange, yellow, green, blue, indigo, violet}\}$

• Normally, two methods are used to represent a set of elements, namely roster form or listing method and set-builder form or rule method.
• In the roster form, all the elements of a set separated with a comma are listed in a row inside the curly brackets.

• In the set builder form, the elements of a set are described by a statement or an expression that represent all the elements.
• All the elements of the set in the set builder form, must have a common property to become the member of that set.

In the given set, the common property is that all are colors and the colors are a part of rainbow.

So, we can write the set in set builder form as

$A = \{x | x~\mbox{ is ~a ~color~ in~ rainbow}\}$

Hence, the given set in set builder form or rule method is $A = \{x | x~\mbox{ is ~a ~color~ in~ rainbow}\}$