Sets

37 lessons

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prerequisite

Ready Check

Make sure you're ready to start

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Are You Ready? Quick Check!

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overview

Why Sets Matter

See sets in your world

Sets Run Your Digital Life

Right now, sets are working behind the scenes:

Your WhatsApp groups? Each is a set of people.

Your Spotify 'Liked Songs'? A set of tracks.

Netflix recommendations? Sets of movies you might like.

Google search results? A set of matching web pages.

Every app, every database, every algorithm uses sets.

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concept

Well-Defined Collections

What makes a set a set?

The Golden Rule

For ANY collection to be a set, this must be true:

Can you clearly decide if something belongs? YES or NO?

No 'maybe'. No 'depends'. No opinions.

Everyone must agree on what's in and what's out.

This is called being well-defined.

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terms

Set Theory Vocabulary

Essential terms and symbols

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concept

Roster Form

Writing sets by listing

Roster Form: Just List Everything

The simplest way to write a set.

List all elements inside curly braces { }.

Separate with commas.

Format: $\{\text{element1, element2, element3, ...}\}$

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concept

Set-Builder Form

Writing sets by describing properties

Set-Builder Form: Describe the Rule

Instead of listing, describe what makes something a member.

Format: $\{x : \text{property of } x\}$

Or: $\{x | \text{property of } x\}$

The colon (:) or bar (|) means 'such that'

Read: 'The set of all x such that [property] is true'

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practice

Practice: Set Representations

Convert between set-builder and roster form

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Express $\{x : x \in \mathbb{N}, x^2 < 20\}$ in roster form:

← previous1.8 Summary overview →NCERT 11 Mathematics

concept

Roster Form

Writing sets by listing

Roster Form: Just List Everything

The simplest way to write a set.

List all elements inside curly braces { }.

Separate with commas.

Format: $\{\text{element1, element2, element3, ...}\}$

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concept

Set-Builder Form

Writing sets by describing properties

Set-Builder Form: Describe the Rule

Instead of listing, describe what makes something a member.

Format: $\{x : \text{property of } x\}$

Or: $\{x | \text{property of } x\}$

The colon (:) or bar (|) means 'such that'

Read: 'The set of all x such that [property] is true'

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practice

Practice: Set Representations

Convert between set-builder and roster form

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Express $\{x : x \in \mathbb{N}, x^2 < 20\}$ in roster form: