Use of Venn Diagrams in Checking Truth and Falsity of Statements
Category : JEE Main & Advanced
In this section, we shall discuss how Venn diagrams are used to represent truth and falsity of statements or propositions. For this, let us consider the statement: “All teachers are scholars”. Let us assume that this statement is true. To represent the truth of the above statement, we define the following sets
\[U\]= the set of all human beings
S = the set of all scholars
And T = the set of all teachers
Clearly, \[S\subset U\] and \[T\subset U\]
According to the above statement , if follows that \[T\subset S\]. Thus, the truth of the above statement can be represented by the Venn diagram shown in
Now, if we consider the statement : ? There are some scholars who are teachers?, It is evident from the Venn diagram that there is a scholar x who is not a teacher. Therefore, the above statement is false and its truth value is ?F?. Thus, we can also check the truth and falsity of other statements which are connected to a given statement.
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