Knowledge organisers

Sets: CBSE Class 11 Maths knowledge organiser

Everything to know about sets on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Set: A well-defined collection of objects, called its elements.
Subset: A ⊂ B when every element of A is also in B.
Complement: A′: the elements of the universal set that are not in A.

Key formulas

Intervals: \((a,b)\), \([a,b]\), \([a,b)\), \((a,b]\); \(A\subset B\): every element of \(A\) is in \(B\)
Difference; complement	\(A-B=A\cap B';\) \(A\cup A'=U,\) \(A\cap A'=\phi\)
De Morgan	\((A\cup B)'=A'\cap B',\) \((A\cap B)'=A'\cup B'\)
Distributive	\(A\cap(B\cup C)=(A\cap B)\cup(A\cap C)\)

Worked example

Write \(\{x : x \in \mathbb Z, x^2 \lt 10\}\) in roster form.

\(x^2 \lt 10\) for \(x = -3, -2, \ldots, 3\): \(\{-3, -2, -1, 0, 1, 2, 3\}\).

Common mistakes

Repeating elements in roster form, or treating \(\{\phi\}\) as empty (it has one element).
Getting the end-points of intervals wrong in intersections and differences.
Writing \((A \cup B)' = A' \cup B'\): De Morgan's laws swap union and intersection.
Confusing \(\in\) (element) with \(\subset\) (subset).

You should be able to…

Switch between roster and set-builder forms, spot empty and equal sets, and use interval notation.
Find unions, intersections, differences and complements, including of intervals, and verify De Morgan's laws.
Prove set identities by elements and answer multi-part Venn-diagram questions.
Reason with subsets and the distributive laws and handle tricky interval end-points.

The printable sheet

Sets knowledge organiser for CBSE Class 11 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Sets knowledge organiser (CBSE Class 11 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 11 Maths topics: Relations and Functions · Trigonometric Functions · Complex Numbers and Quadratic Equations · Linear Inequalities · Permutations and Combinations · Binomial Theorem · Sequences and Series · Straight Lines · Conic Sections · Introduction to Three Dimensional Geometry · Limits and Derivatives · Statistics · Probability · All CBSE Class 11 Maths organisers