Sets

​What is set?

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A set is a collection of well-defined, distinct objects.

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These objects are usually referred to as the elements of the set. Sets are denoted by uppercase letters of the alphabet such as A, B, and C.

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​Study the following sets of numbers:

Set A: All integers from –5 to 5

Set B: All whole numbers from 0 to 5

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An object a is an element of set A if and only if a belongs to set A. In symbols, a ∈ A

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​The elements in a set are the objects in it..

Consequently, an object b is not an element of set A if and only if b does not belong to set A. In symbols,

b ∉ A.

In symbols, if set A consists of all integers from –5 to 5 and set B consists of all whole numbers from 0 to 5, then

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–3∈A​

–3∉B

​Representing Sets

Roster form – All elements of the set are listed and enclosed in braces.

A = {–5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5}

B = {0, 1, 2, 3, 4, 5}

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Set-builder form – A common property of all the elements of the set is written.

Sets A and B in the example above can be written in set-builder form as follows:

A = {x:x is an integer from –5 to 5}

which is read as “A is the set of all x such that x is an integer from –5 to 5,” and

B = {x:x is a whole number from 0 to 5}

which is read as “B is the set of all x such that x is a whole number from 0 to 5.”

​Note: you may use any variable aside from x when you write a set in the set-builder form.

​Choose the correct answer from the box provided to you.

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​Sets Subsets Elements Roaster Form

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Set builder Form​ ∈ Union Intersection

​______1. is a collection of well-defined, distinct objects.

______2. ​The ___________ in a set are the objects in it..