Class 10 Mathematics | Unit 1 Sets Formula & Key Points
Introduction to the Chapter
Welcome to the essential guide for Unit 1 Sets in the Class 10 Compulsory Mathematics curriculum. In the Secondary Education Examination (SEE), this topic forms the foundation for logical reasoning and mathematical structuring. Mastering these formulas is crucial for solving problems related to cardinality, unions, intersections, and complements.
This comprehensive page covers every critical theorem required for solving set problems. We have organized the content to help you distinguish between basic operations with two groups and the more complex scenarios involving three categories.
1. Formulae for Two Subsets (A & B)
The table below summarizes the notations used for two subsets A and B.
| पदावली (Terminology) | समूह सङ्केत (Symbol) |
|---|---|
| n(A मात्र) n(only A) |
$n_o(A)$ |
| n(B मात्र) n(only B) |
$n_o(B)$ |
| n(ठीक एउटा) n(exactly one) |
$n_o(A) + n_o(B)$ |
| n(कम्तीमा एउटा) n(at least one) |
$n(A \cup B)$ |
| n(दुवै) n(both) |
$n(A \cap B)$ |
Fundamental Relations
- (a) $n(\overline{A \cup B}) = n(U) – n(A \cup B)$
- (b) $n(A \cup B) = n(A) + n(B) – n(A \cap B)$
- (c) $n(A \cup B) = n_o(A) + n_o(B) + n(A \cap B)$
- (d) $n_o(A) = n(A) – n(A \cap B)$
- (e) $n_o(B) = n(B) – n(A \cap B)$
2. Difference of Sets
3. $n(\overline{A} \cap B) = n(B – A) = n_o(B)$
4. $n(A \cap \overline{B}) = n(A – B) = n_o(A)$
3. Formulae for Three Subsets
| पदावली (Terminology) | समूह सङ्केत (Symbol) |
|---|---|
| n(A मात्र) n(only A) |
$n_o(A)$ |
| n(ठीक एउटा) n(exactly one) |
$n_o(A) + n_o(B) + n_o(C)$ |
| n(कम्तीमा एउटा) n(at least one) |
$n(A \cup B \cup C)$ |
Three-Set Theorems
(a) Union Expansion:
(b) Alternative Method (Only):
$[n_o(A) + n_o(B) + n_o(C)] +$
$[n_o(A \cap B) + n_o(B \cap C) + n_o(C \cap A)] +$
$n(A \cap B \cap C)$
= n(only one) + n(only two) + n(all three)
(c) $n(\overline{A \cup B \cup C}) = n(U) – n(A \cup B \cup C)$
(d) $n(A \cup B \cup C) = n(A \cup B) + n_o(C)$
Full Chapter PDF Manual
For offline study, access the complete PDF manual below.
Disclaimer
This pdf notes is based on old course but same as most of the question in new course and taken from manual written by:
- Title: Compulsory Maths SEE Manual
- Writer: Dr Simkhada
- Publisher: Readmore Publishers & Distributors
- Edition: 2076
Additional References
For further reading on the mathematics curriculum in Nepal including this chapter, please visit the Ministry of Education, Science and Technology. You can also explore general set theory concepts on Wikipedia.