Write the set using setbuilder notation 25 35 45 55 The let

Write the set using set-builder notation. {25, 35, 45, 55} The let S of numbers that are odd multiples of 5 between 20 and 60. {25, 35, ..., 55} {x | x is an odd multiple of 5 between 20 and 60} The set S of numbers that are odd multiples of 5 between 25 and 55. {x | x is an odd multiple of 5 between 25 and 55}

Solution

Solution :

Before beginning with our solution, we will first try and understand various techniques in which a set can be represented.

Below are the 3 techniques to represent a set :

1. Statement form method.

2. Roster or tabular form method.

3. Rule or set builder form method.

Statement form method.

For this techniques, proper description of the elements of the set is given and the same are enclosed within the curly braces.

For example :

a) The set of even numbers less than 8 is written as : {even numbers less than 8}.

b) A set of hockey players with ages between 19 years to 33 years.

Roster or tabular form method.

For this techniques, elements of the set are mentioned within the curly brackets and seperated by commas.

For example :

a). Let N denotes the first 5 even numbers,

hence, N = {2,4,6,8,10}.

b). Let N denotes the months begining with letter J.

hence, N = {January,June,July}

Rule or set builder form method

As mentioned in the question, our focus will be on this set represantation technique.

For this technique, any rule, formula or any statement which defines the set completly, is written within the pair of brackets. All the elements of the set must have a specific property so as to become a part of the set.

For this type of set representation technique, the elements of the set is described using a symbol \'X\' or any other variable followed by a colon (:) or (|) and then any statement which describes the property of the element of the set. The whole thing is enclosed within the pair of brackets.

Here, colon (:) stands for \"such that\" and braces stands for \"set of all\".

For example :

Let N is a set of even numbers greater than 14,

then, N = {x:x is an even number and greater than 14}

OR N = {x|x is an even number and greater than 14}

So, as we now able to understand all the set represantion technique, we are now able to represent {25,35,45,55} in set builder notation, which would be as below,

{x|x is an odd multiple of 5 between 20 and 60}------------ Answer.

We have not considered, {x|x is an odd multiple of 5 between 25 and 55} as the answer because then elements 25 and 55 would not be included in the set and the set would become as {35,45} which is not the one mentioned in the question.