Day 01 – Discrete mathematics for computer science in Hindi For CSEIT – Power Set with application.
Contents
- 0.1 Discrete Mathematics for Computer Science – Power Set & Its Applications
- 0.2 What is a Power Set?
- 0.3 Example of Power Set
- 0.4 Formula for Power Set Size
- 0.5 Applications of Power Set in Computer Science
- 0.6 Data Security & Cryptography
- 0.7 Machine Learning & AI
- 0.8 Database Query Optimization
- 0.9 Automata Theory & Formal Languages
- 0.10 Set Theory & Logic Gates in Digital Circuits
- 0.11 Summary
- 0.12 Day 01 – Discrete mathematics for computer science in Hindi For CSEIT – Power Set with application.
- 0.13 Computer Science & Engineering Syllabus
- 1 Day 01 – डिस्क्रीट मैथमेटिक्स (Discrete Mathematics) – Power Set
- 2 Power Set क्या है?
- 3 Power Set का प्रयोग (Applications):
- 4 Quick Practice:
Discrete Mathematics for Computer Science – Power Set & Its Applications
Topic: Power Set
Subject: Discrete Mathematics
Useful For: CSE / IT / GATE / Competitive Exams
What is a Power Set?
A Power Set (P(S)) of a given set S is the set of all possible subsets of S, including the empty set (Ø) and the set itself.
If a set S has n elements, then its Power Set will have 2ⁿ subsets.
Example of Power Set
Let’s take a simple set:
S = {a, b}
Subsets of S:
-
Ø (Empty Set)
-
{a}
-
{b}
-
{a, b}
So, the Power Set P(S) = { Ø, {a}, {b}, {a, b} }
Here, S has 2 elements, so the Power Set has 2² = 4 subsets.
Formula for Power Set Size
If a set S has n elements, then the number of subsets in its Power Set is:
∣P(S)∣=2n|P(S)| = 2^n
For example:
If n = 3, then P(S) has 2³ = 8 subsets.
If n = 4, then P(S) has 2⁴ = 16 subsets.
Applications of Power Set in Computer Science
Data Security & Cryptography
Used in encryption algorithms for secure communication.
Helps in defining all possible key combinations.
Machine Learning & AI
Power sets are used in feature selection to evaluate different subsets of data.
Helps in decision trees and pattern recognition.
Database Query Optimization
Used in SQL & NoSQL queries to find all possible combinations of attributes.
Automata Theory & Formal Languages
Helps in defining state transition systems in finite automata.
Used to create regular expressions and context-free grammars.
Set Theory & Logic Gates in Digital Circuits
Used in Boolean algebra for simplifying logic circuits.
Helps in finding all possible input-output combinations.
Summary
Power Set contains all possible subsets of a given set.
Formula: If S has n elements, then P(S) has 2ⁿ subsets.
Applications: Used in cryptography, AI, databases, digital circuits, and automata theory.
Would you like more examples or a detailed explanation in Hindi?
Day 01 – Discrete mathematics for computer science in Hindi For CSEIT – Power Set with application.
Computer Science & Engineering Syllabus
यह रहा Day 01 – Discrete Mathematics for Computer Science (CSE/IT) का एक सरल और स्पष्ट Power Set का पाठ हिंदी में, साथ में इसके Application (प्रयोग) भी दिए गए हैं:
![](data:image/svg+xml;charset=utf-8,<svg height="72" width="72" xmlns="http://www.w3.org/2000/svg" version="1.1"/>)
किसी सेट (Set) के सभी संभावित सब-सेट्स (Subsets) का संग्रह Power Set कहलाता है।
Power Set में खाली सेट (∅) और स्वयं सेट भी शामिल होते हैं।
अगर A कोई सेट है, तो उसका Power Set को P(A) या 2^A से दर्शाया जाता है।
मान लीजिए
A = {1, 2}
तो A के Subsets होंगे:
-
∅
-
{1}
-
{2}
-
{1, 2}
P(A) = { ∅, {1}, {2}, {1, 2} }
(जहाँ n = elements की संख्या)
1.
Power set का प्रयोग Data Analysis, State Machines, Decision Trees, आदि में किया जाता है।
2.
किसी भी प्रॉब्लम के सभी संभव समाधान निकालने के लिए।
3.
किसी रिलेशन के सभी combinations जानने के लिए।
4.
डिसीजन मेकिंग और hypothetical scenario generation के लिए।
Set B = {a, b, c}
Find P(B)?
Answer:
Subsets of B:
-
∅
-
{a}, {b}, {c}
-
{a, b}, {a, c}, {b, c}
-
{a, b, c}
So,
P(B) = {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
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n elements का Power Set = 2ⁿ subsets
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Power Set में हमेशा खाली सेट होता है
-
Power Set का प्रयोग कई computer science fields में होता है
क्या आप इसके लिए एक पीडीएफ नोट्स, क्विज़ या वीडियो लेसन भी चाहेंगे?
![](data:image/svg+xml;charset=utf-8,<svg height="141" width="271" xmlns="http://www.w3.org/2000/svg" version="1.1"/>)