Express the Truth of Each of the Following Statements by Venn Diagram: (A) Some Hardworking Students Are Obedient. (B) No Circles Are Polygons. (C) All Teachers Are Scholars and Scholars Are Teachers. - Mathematics and Statistics

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Sum

Express the truth of each of the following statements by Venn diagram:

(a) Some hardworking students are obedient.

(b) No circles are polygons.

(c) All teachers are scholars and scholars are teachers. 

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Solution

(a) Some hardworking students are obedient.

Let H: set of hardworking students

     O: Set of obedient students

     U: Set of all students

from Venn diagram the truth value is H ∩ O

 

(b) No circles are polygons.

Let C: Set of all circles

     P: Set of all polygons

     U:set of all closed figures

From Venn diagram the truth value is 

C ∩ P= Φ

(c) All teachers are scholars and scholars are teachers. 

Let T: Set of all teachers

     S: Set of all scholars

     U: Set of all human beings

From Venn diagram the truth value is T=S

Concept: Venn Diagrams
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2014-2015 (March)

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