Sets — Part 1: Sets, subsets and intervals: visual lesson, CBSE Class 11 Mathematics

Lesson

Sets, Part 1: Collections with a clear rule

A set is a collection whose membership is settled by a clear rule.

In this lesson you will

Decide when a collection is a set and write it in roster and set-builder form
Classify sets as empty, singleton, finite, infinite or equal
Find subsets and the power set of a finite set
Use the universal set and write intervals of real numbers

A set needs a rule that settles membership.
Collection	Well defined?	Why
Prime numbers below $20$	✓	$\{2, 3, 5, 7, 11, 13, 17, 19\}$
Tall students of the class	✗	No clear rule for "tall"
Vowels of the English alphabet	✓	$\{a, e, i, o, u\}$
Good songs of the year	✗	Opinion, not a rule

Concept

What you will be able to do

Tell a well-defined collection from an opinion
Write sets in roster and set-builder form
Classify empty, finite, infinite and equal sets
List subsets and count the power set
Write intervals on the real line

Concept

Elements and notation

Objects in a set are its elements. We write $a \in A$ for " $a$ belongs to $A$ " and $a \notin A$ otherwise. Capital letters name sets; standard sets are $\mathbb{N}$ , $\mathbb{W}$ , $\mathbb{Z}$ , $\mathbb{Q}$ , $\mathbb{R}$ .

\mathbb{N} \subset \mathbb{W} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}

Each number set is a subset of the next.

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