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 }

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 }

Let *A *= {0,1}, *B *= {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*×*B*)×*C*= {(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.

Tags : Illustration for Geometrical understanding , 10th Mathematics : UNIT 1 : Relation and Function

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10th Mathematics : UNIT 1 : Relation and Function : Cartesian Product of three Set | Illustration for Geometrical understanding

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