Let A be a non-empty set such that A- A has 9 elements among which -2-0-0-2 are found- Then A is equal to

We have ( 2,0) and (0,2) ∈ A× A ⇒{ 2,0,2}→ A nbsp; Also, A× A has 9 elements nbsp; ∴ A={ 2,0,2} nbsp; ...

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Standard XII

Mathematics

Cartesian Product

Let A be a no...

Question

Let $A$ be a non-empty set such that $A \times A$ has $9$ elements among which $(- 2, 0), (0, 2)$ are found. Then $A$ is equal to

{- 2, 0}

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{0, 2}

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{- 2, 0, 2}

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{- 2, - 1, 0, 1, 2}

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Solution

The correct option is C ${- 2, 0, 2}$
We have $(- 2, 0)$ and $(0, 2) \in A \times A$
$\Rightarrow {- 2, 0, 2} \to A$
Also, $A \times A$ has $9$ elements

$∴ A = {- 2, 0, 2}$

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Let A be a non-empty set such that A×A has 9 elements among which (−2,0),(0,2) are found. Then A is equal to

The correct option is C {−2,0,2}We have (−2,0) and (0,2)∈A×A ⇒{−2,0,2}→A Also, A×A has 9 elements ∴A={−2,0,2}

Let $A$ be a non-empty set such that $A \times A$ has $9$ elements among which $(- 2, 0), (0, 2)$ are found. Then $A$ is equal to

The correct option is C ${- 2, 0, 2}$
We have $(- 2, 0)$ and $(0, 2) \in A \times A$
$\Rightarrow {- 2, 0, 2} \to A$
Also, $A \times A$ has $9$ elements

$∴ A = {- 2, 0, 2}$