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Empty Set

The following...

Question

The following is example of empty set:
${x : x^{2} - 2 = 0$ and x is rational $}$ .

True

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False

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Solution

The correct option is A True
Since, $x^{2} - 2 = 0$
$\Rightarrow x^{2} = 2$
$\Rightarrow x = \pm \sqrt{2}$
Since $x$ is satisfied by only irrational number, the given set is an example of 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}.

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.

5

{x : x^{2} - 2 = 0

x

}

{x : x

x < 8

x > 12

{x : x

}

x^{2} = 2

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