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Cartesian Product

Bengali: কার্তেসীয় গুণজ•Pronunciation: কার্তেসীয়ান প্রোডাক্ট•Symbol: A \times B
Standard Definition:
The mathematical set operation returning all ordered pairs (x, y) where x belongs to set A and y belongs to set B.

📐 Mathematical Equation, Units & Dimensions

Defining Mathematical Equation
A×B={(x,y):x∈A এবং y∈B}, n(A×B)=n(A)×n(B)A \times B = \{(x, y) : x \in A \text{ এবং } y \in B\}, \text{ } n(A \times B) = n(A) \times n(B)
Standard SI Unit
Set of ordered pairs(ক্রমজোড়ের সেট)
Dimensional Analysis
[M0L0T0][M^0 L^0 T^0]
CGS Unit
None

📖 Physical Concept & Comprehensive Explanation

The Cartesian product produces ordered pairs bridging set theory with coordinate geometry and mathematical relations. If cardinality of A is p and B is q, then n(A x B) = p * q.

🎯 High-Yield Revision Points

  • ✓Elements consist of ordered pairs (x, y).
  • ✓Cardinality: n(A x B) = n(A) * n(B).
  • ✓Non-commutative: A x B != B x A in general.

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❓ Frequently Asked Exam Questions (FAQ)

Common questions in board and competitive entrance examinations

Q1: What is a Cartesian Product?

A set operation generating all possible ordered pairs from two input sets.

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