State- whether the following set is an example of empty set-iv x-x is a natural number- x12

Name: RDSHA - Grade 11 - Mathematics - Sets - Q11_04
Uploaded: 2022-07-04T10:36:42+05:30
Description: Given, nbsp;x:x is a natural number, amp; nbsp; amp; nbsp; nbsp; x lt;8 and amp; nbsp; amp; simultaneously x gt;12 nbsp; amp; ...

Given, nbsp;x:x is a natural number, amp; nbsp; amp; nbsp; nbsp; x lt;8 and amp; nbsp; amp; simultaneously x gt;12 nbsp; amp; ...

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Byju's Answer

Standard XII

Mathematics

Union

State, whethe...

Question

State, whether the following set is an example of empty set.

(iv) $⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x : x i s a n a t u r a l n u m b e r, x < 8 a n d s i m u l t a n e o u s l y x > 12 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$

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Solution

Given, $⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x : x i s a n a t u r a l n u m b e r, x < 8 a n d s i m u l t a n e o u s l y x > 12 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$

There exist no natural number which is less

than 8 and simultaneously greater than 12.

Thus, it is an example of an empty set.

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Similar questions

Which of the following are examples of empty set ?

(i) Set of all even numbers divisible by 5.

(ii) Set of all even prime numbers.

(iii) { $x : x^{2} = 0$ and x is rational}.

(iv) {x : x is a natural number, x < 8 and simultaneously x > 12}.

(v) {x : x is a point common to any two parallel lines}.

Q. Which of the following are examples of empty set?
(i) Set of all even natural numbers divisible by 5;
(ii) Set of all even prime numbers;
(iii) {x : x² −2 = 0 and x is rational};
(iv) {x : x is a natural number, x < 8 and simultaneously x > 12};
(v) {x : x is a point common to any two parallel lines}.

Q. Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(i) {

x : x

is an even natural number}

(ii) {

x : x

is an odd natural number}

(iii) {

x : x

is a positive multiple of

3

}

(iv) {

x : x

is a prime number }

(v) {

x : x

is a natural number divisible by

3

and

5

}

(vi) {

x : x

is a perfect square }

(vii) {

x : x

is a perfect cube}

(viii)

{x : x + 5 = 8}

(ix)

{x : 2 x + 5 = 9}

(x)

{x : x \geq 7}

(xi)

{x : x ϵ N a n d 2 x + 1 > 10}

Q. State whether given set is empty or not?

{x : x

is a natural numbers,

x < 5

and

x > 7}

State, whether the following set is an example of empty set.
(iii) ${x : x^{2} - 2 = 0 and x is rational}$

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Union

Standard XII Mathematics

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State, whether the following set is an example of empty set. (iv) ⎧⎪⎨⎪⎩x:x is a natural number,x<8 and simultaneously x>12⎫⎪⎬⎪⎭

Given, ⎧⎪⎨⎪⎩x:x is a natural number,x<8 and simultaneously x>12⎫⎪⎬⎪⎭ There exist no natural number which is less than 8 and simultaneously greater than 12. Thus, it is an example of an empty set.

State, whether the following set is an example of empty set.

(iv) $⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x : x i s a n a t u r a l n u m b e r, x < 8 a n d s i m u l t a n e o u s l y x > 12 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$

Given, $⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x : x i s a n a t u r a l n u m b e r, x < 8 a n d s i m u l t a n e o u s l y x > 12 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$

There exist no natural number which is less

than 8 and simultaneously greater than 12.

Thus, it is an example of an empty set.