If A -1-1- find A - A - A-

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

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Standard XII

Mathematics

Cartesian Product

If A =-1,1, f...

Question

If A = {-1, 1}, find $A \times A \times A$ .

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Solution

We have,

A = {-1, 1}

$∴ A \times A = {- 1, 1} \times {- 1, 1}$

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

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

$= {(- 1, - 1, - 1), (- 1, - 1, 1), (- 1, 1, - 1),$

$(- 1, 1, 1), (1, - 1, - 1), (1, - 1, 1), (1, 1, - 1), (1, 1, 1)}$

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If A = {-1, 1}, find A×A×A.

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

If A = {-1, 1}, find $A \times A \times A$ .