Set, Relations & Functions

Goal of this chapter: By the end of this lesson, you will feel confident with the key NDA-level concepts of Set, Relations & Functions and be able to solve exam-style questions on your own.

हिंदी Note: इस chapter को आराम से पढ़िए – examples और छोटे-छोटे अभ्यास के साथ। एक बार समझ आ गया तो NDA में Set, Relations & Functions के सवाल आपके लिए बहुत आसान हो जाएंगे 😄

Overview / परिचय

English: This chapter helps understand the basic building blocks of mathematics — sets, how elements relate within or across sets, and how functions map values from one set to another.

हिंदी: यह अध्याय गणित की मूलभूत अवधारणाओं जैसे कि सेट्स, उनके बीच संबंध एवं फंक्शन्स को समझने में मदद करता है।

Important Formulas & Tricks / महत्वपूर्ण सूत्र और ट्रिक्स

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(C ∩ A) + n(A ∩ B ∩ C)
Number of relations from A to B = m × n (where |A| = m, |B| = n)
Number of functions from A to B = n^m

Practice Questions with Hints / प्रैक्टिस प्रश्न संकेतों के साथ

Q1: If A = {1, 2, 3}, B = {4, 5}, how many functions are there from A to B?

Hint: Use n^m, here n = 2 (B), m = 3 (A).

Q2: If n(A) = 25, n(B) = 30, and n(A ∩ B) = 10, find n(A ∪ B).

Hint: Apply the formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

Q3: If n(A) = 15, n(B) = 10, how many relations can be defined from A to B?

Hint: Number of relations = m × n

Q4: A = {1, 2}, B = {x, y, z}. How many one-one functions can be formed from A to B?

Hint: Use permutation P(n, r) = n! / (n-r)!

Q5: A survey shows 60 people like tea, 40 like coffee, and 20 like both. How many like either tea or coffee?

Hint: Use union formula with intersection.

Additional Practice Questions / अतिरिक्त अभ्यास प्रश्न

Find the number of functions from a set with 4 elements to a set with 3 elements. Answer: 81
In a class, 20 students take Math, 15 take English, and 5 take both. How many students take at least one? Answer: 30
If A has 5 elements and B has 2 elements, how many relations exist from A to B? Answer: 10
Number of one-one functions from set {a, b} to {1, 2, 3}? Answer: 6
How many subsets does a set with 4 elements have? Answer: 16

Ask Doubt

Quick Recap | सार

Now you should be able to:

Recall the key ideas of this chapter without looking at the book.
Solve most NDA-style questions of this topic step by step.
Identify and avoid the most common traps used in competitive exams.

Self-check: अगर practice questions अपने आप हो रहे हैं, तो chapter strong है। जो सवाल अटकते हैं, बस उन्हें दोबारा देख लें।

Common Exam Mistakes | आम गलतियाँ

जल्दी-जल्दी में question पूरा पढ़े बिना solve करना।
Sign (+/−) या power गलत लिख देना।
Last step में calculation check न करना – आधा काम सही, answer गलत।

ध्यान रखिए: NDA में topper वो नहीं जो सब कुछ जानता है, बल्कि वो है जो छोटी-छोटी गलतियाँ avoid कर देता है।