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De Morgan's Law

Find, which o...

Question

Find, which of the following sets are empty:

C ={even numbers between 6 and 10}

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Solution

Step : Check whether the given set is empty

Given: C = {even numbers between 6 and 10}

We know that a set that does not contain any element is called an empty set or a null set.

Even number between 6 and 10 is 8

$\Rightarrow$ C = {8}

Since number of elements in set C =1

Hence, the given set is not an empty set.

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Similar questions

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 which of the following are null or empty sets?

$\{E v e n n u m b e r w h i c h a r e p r i m e\}$

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. Say true or false:

C = {even numbers between 6 and 10} is not an empty set.

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De Morgan's Law

Standard XII Mathematics

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