Sets — Class 9 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Sets, written for Class 9 Maharashtra SSC 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
a well defined collection, the ways of writing one, and what happens when two are combined
What makes a collection a set
- a set is a well defined collection of distinct objects, and each object in it is called an element
- well defined means there is no argument about membership: the collection of prime numbers under 20 is a set, the collection of tall students is not
- sets are named with capital letters and elements with small ones, so A is the set holding 1, 2 and 3, written inside braces
- a ∈ A is read as a belongs to A, and a ∉ A as a does not belong to A
- elements are not repeated: a roster listing 1, 2, 2 and 3 is simply the set holding 1, 2 and 3
- order does not matter, so a roster reading 1, 2, 3 and one reading 3, 1, 2 describe the same set
Two ways to write the same set
- list every element inside braces, separated by commas
- A is the roster holding 2, 3, 5, 7 and 11
- clear and direct, but impractical for a large set
- for an endless set, three dots stand for the rest, as in the naturals 1, 2, 3 and onwards
- state the rule the elements satisfy
- A is the set of all x such that x is prime and x is under 12
- the bar inside the braces is read as such that
- compact, and it works however large the set is
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Sets sheet covers
- Set
- Element
- Well defined collection
- What makes a collection a set
- Two ways to write the same set
- Roster form
- Set builder form
- Empty set
- Finite and infinite sets
- Subset
- Equal sets
- The kinds of set worth naming
- Union
- Intersection
- Disjoint sets
- Combining two sets
- Counting the elements
- the number of elements in a set A
- elements of a union, overlap removed once
- when the two sets are disjoint
- elements in A but not in B
- number of subsets of a set with n elements
- A counting problem
- Filling a Venn diagram in the right order
- Reading the words into symbols
- Symbols in this 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.