Let A - x - R - x 3-1and B - x - R - x 2-1- thenA- A and B are disjoint-B- A - BC- A - BD- B - A

The correct option is B A ⊂ BA={x ∈ R: x^3=1} x^3 1=0 ⇒ (x 1)(x^2+x+1)=0 ⇒ x=1 [∵ x ∈ R] ∴ A={1} B={x ∈ R: x^2=1} nbsp; nbsp; B={ 1,1} nbsp; nbsp; ...

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Byju's Answer

Standard VI

Mathematics

Idea of a Set

Let A = x ∈ R...

Question

$Let A = {x \in R : x^{3} = 1}$
$and B = {x \in R : x^{2} = 1}, then$

A \subset B

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A = B

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B \subset A

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A

and

B

are disjoint.

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Solution

The correct option is A $A \subset B$
$A = {x \in R : x^{3} = 1}$
$x^{3} - 1 = 0$
$\Rightarrow (x - 1) (x^{2} + x + 1) = 0$
$\Rightarrow x = 1 [∵ x \in R]$
$∴ A = {1}$

$B = {x \in R : x^{2} = 1}$
$B = {- 1, 1}$

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Similar questions

Let A = {x \in R : x^{3} = 1}

and B = {x \in R : x^{2} = 1}, then

Q. Which of the following sets are equal?
(i)

A = \{1, 2, 3\};

(ii)

B = \{x \in R : x^{2} - 2 x + 1 = 0\};

(iii)

C = \{1, 2, 2, 3\};

(iv)

D = \{x \in R : x^{3} - 6 x^{2} + 11 x - 6 = 0\}

Which of the following sets are equal ?

(i) A = {1, 2, 3}

(ii) B = { $x ϵ R : x^{2} - 2 x + 1 = 0$ }

(iii) C = {1, 2, 2, 3}

(iv) D = { $x ϵ R : x^{3} - 6 x^{2} + 11 x - 6 = 0$ }.

Q. Let

A = {x : x i s r e a l s a t i s f y i n g \frac{x}{4} < \frac{5 x - 2}{3} - \frac{(7 x - 3)}{5}}

and

B = {x : x i s r e a l s a t i s f y i n g \frac{2 x}{2 x^{2} + 5 x + 2} > \frac{1}{x + 1}}

, then

If sets A and B are defined as
$A = {(x, y) | y = \frac{1}{x}, x \neq 0, x ϵ R}, B = {(x, y) | y = - x, x ϵ R}$ , then

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Let A={x ∈R:x3=1} and B={x ∈R:x2=1},then

The correct option is A A⊂BA={x ∈R:x3=1} x3−1=0 ⇒(x−1)(x2+x+1)=0 ⇒x=1 [∵x∈R] ∴A={1} B={x ∈R:x2=1} B={−1,1}

$Let A = {x \in R : x^{3} = 1}$
$and B = {x \in R : x^{2} = 1}, then$

The correct option is A $A \subset B$
$A = {x \in R : x^{3} = 1}$
$x^{3} - 1 = 0$
$\Rightarrow (x - 1) (x^{2} + x + 1) = 0$
$\Rightarrow x = 1 [∵ x \in R]$
$∴ A = {1}$

$B = {x \in R : x^{2} = 1}$
$B = {- 1, 1}$