Question

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. 

Answer 1

(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