Sets — Class 11 ISC Mathematics revision notes
A 3-page visual revision sheet for Sets, written for Class 11 ISC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Sets in one look
the language everything after this is written in
What a set is, and the two ways of writing one
- a set is a well defined collection: for any object the question does it belong has exactly one answer, which is why the collection of tall people is not a set
- roster form lists the members inside braces, set builder form states the property, and both describe the same object
- order does not matter and repetition does not count, so the roster of the letters of MISSISSIPPI has just four members
- ∈ means belongs to and ⊂ means is a subset of, and confusing an element with a one element set is the commonest early slip
The kinds of set worth naming
- empty set has no elements at all, written ∅, and it is a subset of EVERY set
- singleton has exactly one; finite and infinite by whether the counting stops
- equal sets have exactly the same members; equivalent sets merely have the same number of members
- universal set U is whatever the discussion is confined to, and every complement is taken with respect to it
- power set P(A) is the set of ALL subsets of A, and it has 2^n members when A has n. It always contains the empty set and A itself
The counting facts
- subsets of a set of n elements
2^n - proper subsets
2^n - 1, since A itself is excluded - subsets of size r
C(n, r) - two sets
n(A ∪ B) = n(A) + n(B) - n(A ∩ B) - three sets
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(C ∩ A) + n(A ∩ B ∩ C)
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Sets sheet covers
- What a set is, and the two ways of writing one
- The kinds of set worth naming
- The counting facts
- subsets of a set of n elements
- proper subsets
- subsets of size r
- two sets
- three sets
- The operations
- The laws, which are worth proving once and quoting after
- Venn diagrams, used properly
- Intervals, which are sets of real numbers
- The number sets, nested
- Survey problems, the standard application
- Cartesian products, the bridge to the next chapter
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Sets the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.