XI - 2.1 Cartesian product of sets - Video Lectures

XI - 2.1 Cartesian product of sets - Video Lectures

2.1 Cartesian product of sets

Cartesian product is an operation on sets.


Ordered pair: An Ordered pair consists of two objects or elements in a given fixed order.

Cartesian product: Let A and B be any two non empty sets. The set of all ordered pairs (a,b) such that a ЄA and b ЄB is called the Cartesian product of the sets A and B and is denoted by A×B

Theorems

Theorem 1; For any three sets

(i) A×(B U C) = (A×B) U (A×C)
(ii) A×(B∩C) = (A×B) ∩(A×C)

Theorem 2: For any three sets

A×(B – C) = (A×B) – (A×C)

Theorem 3: If and A and B are any two non-empty sets, then

A×B = B×A => A = B

Theorem 4: If A is a subset of B, A×A is a sub set of (A×B) ∩(B×A)
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