Question

B = { 6, 12, 18, 24, 30, 36, 42, 48} Write the given sets using rule method.

Answer 1

B={x ∣ x=6y,y ϵ N and 1≤y≤8}

Rule is a method of naming a set by describing its elements.

• { x: x > 3, x is a whole number} describes the set with elements 4, 5, 6,…. Therefore, { x: x > 3, x is a whole number} is the same as {4,5,6,…}. { x: x > 3} describes all numbers greater than 3. This set of numbers cannot be represented as a list and is represented using a number line graph.

Rule method is known as set builder form.

• It is possible to describe a set by specifying its properties rather than just listing its elements using Set Builder Notations. Set abstraction, comprehension, and set an intention are the terms used to describe set building in a set builder notation.
• One or two variables are present in the set builder notation, which additionally specifies which elements are part of the set and which ones are not. A slash and colon divide the rule from the variables. This is frequently employed to describe infinite sets.

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Answer 2

Concept

The rule method of writing a set is a method of naming a set by describing the elements in it.

Given

B = { 6, 12, 18, 24, 30, 36, 42, 48}

Find

We need to rewrite set B using rule method

Solution

We have,

B = { 6, 12, 18, 24, 30, 36, 42, 48}

As we can observe here

6 = 1*6

12 = 2*6

18 = 3*6

and so on up till 48 = 8*6

So we can see that in set B numbers are taken from 1 to 8 and multiplied by 6. We can represent this as follows

B={x ∣ x=6y,y ϵ N and 1≤y≤8}

Thus,  B = { 6, 12, 18, 24, 30, 36, 42, 48} can be written as B={x ∣ x=6y,y ϵ N and 1≤y≤8}

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