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Chapter: 10th Mathematics : Relation and Function

Illustration for Geometrical understanding | Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail |

Cartesian Product of three Set

If A, B, C are three non-empty sets then the cartesian product of three sets is the set of all possible ordered triplets given by A× B ×C= {(a,b,c) for all a ∈ A,b ∈ B,c ∈ C }

Cartesian Product of three Set

If A, B, C are three non-empty sets then the cartesian product of three sets is the set of all possible ordered triplets given by

A× B ×C= {(a,b,c) for all a  A,b  B,c  C }

 

Illustration for Geometrical understanding of cartesian product of two and three sets

Let = {0,1}, = {0,1}, C  = {0,1}

A×B  = {0,1}×{0,1} = {(0, 0),(0,1),(1, 0),(1,1)}


Representing A×B  in the xy - plane we get a picture shown in Fig. 1.5.

(A×BC= {(0, 0),(0,1),(1, 0),(1,1)} ×{0,1}

= {(0, 0, 0),(0, 0,1),(0,1, 0),(0,1,1),(1, 0, 0),(1, 0,1)(1,1, 0),(1,1,1)}

 Representing A×B ×C  in the xyz - plane we get a picture as shown in Fig. 1.6


Thus, A×B  represent vertices of a square in two dimensions and A×B ×C  represent vertices of a cube in three dimensions.

 

NOTES

 In general, cartesian product of two non-empty sets provides a shape in two dimensions and cartesian product of three non-empty sets provide an object in three dimensions.

 

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Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail


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