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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Solution

Given, ${x : x^{2} - 2 = 0 and x is rational}$

Since $x^{2} - 2 = 0$

$\Rightarrow x^{2} = 2$

$\Rightarrow x = \pm \sqrt{2}$

Therefore, $x$ is irrational.

Thus, given set is an empty set.

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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}.

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}.

Find, which of the following sets are empty:

(i)The set of points of intersection of two parallel lines.

(ii) $A = {x : x \in N a n d 5 < x \leq 6}$

(iii) $B = {x : x^{2} + 4 = 0, x \in N}$

(iv) $C = {e v e n n u m b e r s b e t w e e n 6 & 10}$

(v) $D = {p r i m e n u m b e r s b e t w e e n 7 & 11}$

Note : The set, which has no element in it, is called the empty or null set.

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

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

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

(ii) Set of all even prime numbers

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Rational Numbers

Standard IX Mathematics

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State, whether the following set is an example of empty set. (iii) {x:x2−2=0 and x is rational}

Given, {x:x2−2=0 and x is rational} Since x2−2=0 ⇒x2=2 ⇒x=±√2 Therefore, x is irrational. Thus, given set is an empty set.

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

Given, ${x : x^{2} - 2 = 0 and x is rational}$

Since $x^{2} - 2 = 0$

$\Rightarrow x^{2} = 2$

$\Rightarrow x = \pm \sqrt{2}$

Therefore, $x$ is irrational.

Thus, given set is an empty set.