If A -3-5 and A - B - B - A- then the correct options can be A- B - x - x 2-8 x -15-0B- B - x - x -4-1C- B - x - x is prime factor of 15 D- B - x - x - N - 3 - x - 5

The correct options are A B={x: x^2 8x+15=0} B B={x: |x 4|=1} C B={x: x is prime factor of 15}Here, nbsp;A× B=B× A A=B B={x: x^2 8x+15=0} ⇒ nbsp;x^2 8x+15=0 ...

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Byju's Answer

Standard XII

Mathematics

Number of Elements in a Cartesian Product

If A =3,5 and...

Question

If $A = {3, 5}$ and $A \times B = B \times A$ , then the correct option(s) can be

B = {x : x^{2} - 8 x + 15 = 0}

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B = {x : | x - 4 | = 1}

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B = {x : x is prime factor of 15}

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B = {x : x \in N, 3 \leq x \leq 5}

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Solution

The correct options are
A $B = {x : x^{2} - 8 x + 15 = 0}$
B $B = {x : | x - 4 | = 1}$
C $B = {x : x is prime factor of 15}$
Here, $A \times B = B \times A ⟹ A = B$
$B = {x : x^{2} - 8 x + 15 = 0}$
$\Rightarrow x^{2} - 8 x + 15 = 0$
$\Rightarrow x^{2} - 3 x - 5 x + 15 = 0$
$\Rightarrow (x - 3) (x - 5) = 0$
$\Rightarrow x = 3, 5$
$B = {3, 5}$

$B = {x : | x - 4 | = 1}$
$\Rightarrow | x - 4 | = 1$
$\Rightarrow x - 4 = \pm 1$
$\Rightarrow x = 3, 5$
$B = {3, 5}$

$B = {x : x is prime factor of 15}$
Factors of $15$ is ${1, 3, 5, 15}$
Prime factors are ${3, 5}$
$B = {3, 5}$

$B = {x : x \in N, 3 \leq x \leq 5}$
$\Rightarrow x = 3, 4, 5$
$B = {3, 4, 5}$

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If A={3,5} and A×B=B×A, then the correct option(s) can be

If $A = {3, 5}$ and $A \times B = B \times A$ , then the correct option(s) can be