If A -1-2- form the set A - A - A

We have, A = {1, 2} ∴ A × A = {1, 2}×{1, 2} = {(1, 1), (1, 2), (2, 1), (2, 2)} ∴ A × A × A = (1, 2) ×{(1, 1), (1, 2), (2, 1), (2, 2)} = {(1, 1, 1), (1, 1, 2), ...

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Standard XII

Mathematics

Cartesian Product

If A =1,2, fo...

Question

If A = {1, 2}, form the set $A \times A \times A$

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Solution

We have,

$A = {1, 2}$

$∴ A \times A = {1, 2} \times {1, 2}$

$= {(1, 1), (1, 2), (2, 1), (2, 2)}$

$∴ A \times A \times A = (1, 2) \times {(1, 1), (1, 2), (2, 1), (2, 2)}$

$= {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}$

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If A = {1, 2}, form the set A×A×A

We have, A={1,2} ∴A×A={1,2}×{1,2} ={(1,1),(1,2),(2,1),(2,2)} ∴A×A×A=(1,2)×{(1,1),(1,2),(2,1),(2,2)} ={(1,1,1),(1,1,2),(1,2,1),(1,2,2),(2,1,1),(2,1,2),(2,2,1),(2,2,2)}

If A = {1, 2}, form the set $A \times A \times A$

We have,

$A = {1, 2}$

$∴ A \times A = {1, 2} \times {1, 2}$

$= {(1, 1), (1, 2), (2, 1), (2, 2)}$

$∴ A \times A \times A = (1, 2) \times {(1, 1), (1, 2), (2, 1), (2, 2)}$

$= {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}$