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 = Ø

(c) All teachers are scholars and scholars are teachers.
Let  T : Set of a ll teachers
       S : Set of all scholars
      U : S et of all human beings.

∴ From Venn diagram the truth value is T = S.