# State whether the following statement is correct or incorrect. Write the correct form if the incorrect statement: \[\phi \in \{ a,b\} \]

Answer

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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

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