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| रिक्त समुच्चय अद्वितीय समुच्चय है जिसमें कोई अवयव नहीं होता है जैसे कि इसकी कार्डिनैलिटी 0 है। | | रिक्त समुच्चय अद्वितीय समुच्चय है जिसमें कोई अवयव नहीं होता है जैसे कि इसकी कार्डिनैलिटी 0 है। |
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| The empty set is the unique set having no elements such that its cardinality is 0.
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| == Definition ==
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| A set which does not contain any element is called the empty set or the null set or the void set.
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| In set theory, an empty set may be used to classify a whole number between 6 and 7. Since this example does not have any definite answer, it can be represented using an empty set or a null set.
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| Let's consider the following examples where we need to determine if the given sets are empty sets.
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| a.) <math>X=\{x:x</math> is a prime number and <math>14<x<16\}</math>
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| We will consider the set of prime numbers as <math>A</math>. Thus <math>A=\{2,3,5,7,11,13,17...\}</math>. Since there are no prime numbers between <math>14</math> and <math>16</math>, we can conclude that the <math>X</math> is an empty set.
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| b.) Number of vans with 10 doors.
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| In real life, unless there is a situation where a van manufacturing company creates a particular model, it’s impossible to find a van that has 10 doors. So, the set containing the van with 10 doors is an empty set.
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| == Cardinality of Empty Set ==
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| Cardinality can be defined as the size of the set or the total number of elements that are present in a set. As empty sets do not contain any elements, we can say that their cardinality is zero.
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| == How To Represent an Empty Set? ==
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| An empty set is represented as <math>\{\}</math>, containing no element at all. It is also represented using the symbol <math>\varnothing</math> (read as 'phi').
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| (i) Let <math>A=\{x:1<x<2 ,x</math> is a natural number<math>\}</math> Then <math>A</math> is the empty set, because there is no natural number between <math>1</math> and <math>2</math>.
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| (ii) <math>D=\{x:x^2=4,x</math> is odd <math>\}</math>.Then <math>D</math> is the empty set, because the equation <math>x^2=4</math> is not satisfied by any odd value of <math>x</math>
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| [[Category:समुच्चय]][[Category:कक्षा-11]][[Category:गणित]] | | [[Category:समुच्चय]][[Category:कक्षा-11]][[Category:गणित]] |
