Answer
436.5k+ views
Hint: To define this first we have to know what is an empty set and how it is denoted.Empty set is denoted as \[\phi \]
Complete step by step solution:
The empty set is a unique set having no element, its size and cardinality is zero.
The symbol of empty set is $\{ \;\} $ or \[\phi \]
For Example:
A. \[{\text{M = }}\](\[{\text{d: d > 8, d}}\] is the number of days in a week)
Explanation:
Here,\[{\text{d}}\]is greater than\[8\].So, this set (\[{\text{M}}\]) is an empty set because there are only\[7\]days in a week.
B. The set of squares with$5$sides
Explanation:
The figure is shown as a square in which it is clear that the square has four sides. So, it is impossible to have $5$ sides of square as a figure which have five sides that figure is known as pentagon
Properties of empty set:-
1. The empty set is a subset of${\text{A}}$:
\[\forall A:\phi \subseteq A\]
2. The union of${\text{A}}$with the empty set is${\text{A}}$:
\[\forall A:A \cup \phi = A\]
3. The intersection of${\text{A}}$with the empty set is the empty set
\[\forall A:A \cap \phi = \phi \]
4. The Cartesian product of${\text{A}}$and the empty set is the empty set
\[\forall A \times \phi = \phi \]
Note: Take care to see that when giving example of an empty set in rule method,when expanded the set should have no elements in it
Complete step by step solution:
The empty set is a unique set having no element, its size and cardinality is zero.
The symbol of empty set is $\{ \;\} $ or \[\phi \]
For Example:
A. \[{\text{M = }}\](\[{\text{d: d > 8, d}}\] is the number of days in a week)
Explanation:
Here,\[{\text{d}}\]is greater than\[8\].So, this set (\[{\text{M}}\]) is an empty set because there are only\[7\]days in a week.
B. The set of squares with$5$sides
![seo images](https://www.vedantu.com/question-sets/8a2c7724-23e1-47bb-8461-007b9b0885a47756978345101264508.png)
Explanation:
The figure is shown as a square in which it is clear that the square has four sides. So, it is impossible to have $5$ sides of square as a figure which have five sides that figure is known as pentagon
![seo images](https://www.vedantu.com/question-sets/de07e08a-2484-4f9a-a3fe-97ce69db74d4885229967491139589.png)
Properties of empty set:-
1. The empty set is a subset of${\text{A}}$:
\[\forall A:\phi \subseteq A\]
2. The union of${\text{A}}$with the empty set is${\text{A}}$:
\[\forall A:A \cup \phi = A\]
3. The intersection of${\text{A}}$with the empty set is the empty set
\[\forall A:A \cap \phi = \phi \]
4. The Cartesian product of${\text{A}}$and the empty set is the empty set
\[\forall A \times \phi = \phi \]
Note: Take care to see that when giving example of an empty set in rule method,when expanded the set should have no elements in it
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)