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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

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