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Formula Sheet

Sets — Formula Sheet

IISER Aptitude Test · Mathematics

Free Sets formula sheet for IISER Aptitude Test Mathematics 2026 — all important formulas, equations, and constants for quick reference.

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A comparison illustrating how the same set can be represented using the Roster (listing) method and the Set-Builder method, with clear examples.
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Formula Sheet — Sets

Important formulas and equations from Sets for IISER Aptitude Test Mathematics.

Formulas — Sets

Set Representations and Basic Concepts

A = {x : P(x)}
n(P(A)) = 2^n

Subsets and Intervals

Number of proper subsets = 2^n - 1
Length of interval = b - a

Operations on Sets

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)
n(A - B) = n(A) - n(A ∩ B)
n(A Δ B) = n(A) + n(B) - 2n(A ∩ B)

Advanced Counting Formulas

Exactly two sets = n(A∩B) + n(B∩C) + n(A∩C) - 3n(A∩B∩C)
Exactly one set = n(A) + n(B) + n(C) - 2[n(A∩B) + n(B∩C) + n(A∩C)] + 3n(A∩B∩C)
n(A' ∪ B') = n(U) - n(A ∩ B)
n(A' ∩ B') = n(U) - n(A ∪ B)

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Frequently Asked Questions

What topics are covered in Sets for IISER Aptitude Test?
Sets is an important chapter in IISER Aptitude Test Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Basic Concepts and Representations, Subsets and Power Sets, Set Operations - Union and Intersection, Complement and Difference Operations.
How important is Sets for IISER Aptitude Test?
Sets is a frequently tested chapter in IISER Aptitude Test Mathematics. Questions from this chapter appear regularly in previous year papers. There are 172 practice questions available for this chapter.
How to prepare Sets for IISER Aptitude Test?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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