State whether the following statement is correct or incorrect. Write the correct form if the incorrect statement: \[\phi \in \{ a,b\} \]
Answer
327.3k+ views
Hint: You need to know what the symbol \[\phi \] denotes. Then you need to analyse if the following statement is true or false.
Complete step-by-step answer:
Set is a collection of well-defined objects. It is denoted by writing its elements within the braces. Example of a set is {a, b, 2, 4}.
We say that an object or element belongs to a set if it contains that object. For example, 1 belongs to the set {1, 2}.
The elements inside a set are separated by commas and each element is unique, there is no duplicate.
We also know few examples where the elements do not belong to a given set, for example, 1 does not belong to the set {{1},2} since, {1} is the element of it and not 1. Also, we don’t say {1} belongs to the set {1, 2}.
Then, we come across subsets. A subset S of another set A is defined as a set which contains element that belongs only to A. For example, {1} is a subset of {1,2}, then we write \[\{ 1\} \subset \{ 1,2\} \].
We know that the null set {}, which is also denoted by \[\phi \], is a subset of every set.
The given statement is \[\phi \in \{ a,b\} \], that is {} belongs to {a, b}, meaning {} is an element of the set {a, b} which is wrong because \[\phi \] is a subset of {a, b} and not an element itself.
Therefore, the correct statement is as follows:
\[\phi \subset \{ a,b\} \]
Note: You may wrongly conclude that \[\phi \in \{ a,b\} \] is the correct statement which is wrong. You might also rewrite the statement as \[\phi \notin \{ a,b\} \], which is also a correct answer.
Complete step-by-step answer:
Set is a collection of well-defined objects. It is denoted by writing its elements within the braces. Example of a set is {a, b, 2, 4}.
We say that an object or element belongs to a set if it contains that object. For example, 1 belongs to the set {1, 2}.
The elements inside a set are separated by commas and each element is unique, there is no duplicate.
We also know few examples where the elements do not belong to a given set, for example, 1 does not belong to the set {{1},2} since, {1} is the element of it and not 1. Also, we don’t say {1} belongs to the set {1, 2}.
Then, we come across subsets. A subset S of another set A is defined as a set which contains element that belongs only to A. For example, {1} is a subset of {1,2}, then we write \[\{ 1\} \subset \{ 1,2\} \].
We know that the null set {}, which is also denoted by \[\phi \], is a subset of every set.
The given statement is \[\phi \in \{ a,b\} \], that is {} belongs to {a, b}, meaning {} is an element of the set {a, b} which is wrong because \[\phi \] is a subset of {a, b} and not an element itself.
Therefore, the correct statement is as follows:
\[\phi \subset \{ a,b\} \]
Note: You may wrongly conclude that \[\phi \in \{ a,b\} \] is the correct statement which is wrong. You might also rewrite the statement as \[\phi \notin \{ a,b\} \], which is also a correct answer.
Last updated date: 31st May 2023
•
Total views: 327.3k
•
Views today: 6.83k
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
