JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Use of Venn Diagrams in Checking Truth and Falsity of Statements

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.