Exercise 1.10 (1)
1. Represent the truth of each of the following statements by Venn diagrams.
i) Some hardworking students are obedient.
Ans:
Let
U : The set of all students.
H : The set of all hardworking Students.
O : The set of all obedient students.
The venn diagram represents truth of the given statement, i.e H∩O≠∅
ii) No circles are polygons.
Ans:
Let
U : The set of all closed geometrical figures in plane.
P : The set of all polygons
C : The set of all circles.
The venn diagram represents truth of the given statement, i.e P∩C=∅
iii) All teachers are scholars and scholars are teachers.
Ans:
Let
U : The set of all human beings.
T : The set of all teachers
S : The set of all Scholars
The venn diagram represents truth of the given statement, i.e T=S
iv) If a quadrilateral is a rhombus, then it is a parallelogram.
Ans:
Let
U : The set of all quadrilaterals.
P : The set of all parallelograms.
R : The set of all rhombuses.
The venn diagram represents truth of the given statement, i.e R⊂P