Balbharati Maharashtra State Board 12th Commerce Maths Solution Book Pdf Chapter 1 Mathematical Logic Ex 1.10 Questions and Answers.

## Maharashtra State Board 12th Commerce Maths Solutions Chapter 1 Mathematical Logic Ex 1.10

Question 1.

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

(i) Some hardworking students are obedient.

Solution:

Let U : set of all students

S : set of all hardworking students

O : set of all obedient students.

Then the Venn diagram represents the truth of the given statement is as below:

S ∩ O ≠ φ

(ii) No circles are polygons.

Solution:

Let U : set of closed geometrical figures in the plane

P : set of all polygons

C : set of all circles.

Then the Venn diagram represents the truth of the given statement is as follows:

P ∩ C = φ

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

Solution:

Let U : set of all human beings

T : set of all teachers

S : set of all scholars.

Then the Venn diagram represents the truth of the given statement is as below:

(iv) If a quadrilateral is a rhombus, then it is a parallelogram.

Solution:

Let U : set of all quadrilaterals

R : set of all rhombus

P : set of all parallelograms.

Then the Venn diagram represents the truth of the given statement is as below:

R ⊂ P

Question 2.

Draw the Venn diagrams for the truth of the following statements:

(i) Some share brokers are chartered accountants.

Solution:

Let U : set of all human beings

S : set of all share brokers

C : set of all chartered accountants.

Then the Venn diagram represents the truth of the given statement is as below:

S ∩ C ≠ φ

(ii) No wicket-keeper is a bowler in a cricket team.

Solution:

Let U : set of all human beings

W : set of all wicket keepers

B : set of all bowlers.

Then the Venn diagram represents the truth of the given statement is as follows:

W ∩ B = φ

Question 3.

Represent the following statements by Venn diagrams:

(i) Some non-resident Indians are not rich.

Solution:

Let U : set of all human beings

N : set of all non-resident Indians

R : set of all rich people.

Then the Venn diagram represents the truth of the given statement is as below:

N – R ≠ φ

(ii) No circle is a rectangle.

Solution:

Let U : set of all geometrical figures

C : set of all circles

R : set of all rectangles

Then the Venn diagram represents the truth of the given statement is as below:

C ∩ R = φ

(iii) If n is a prime number and n ≠ 2, then it is odd.

Solution:

Let U : set of all real numbers

P : set of all prime numbers n, where n ≠ 2

O : set of all odd numbers.

Then the Venn diagram represents the truth of the given statement is as below:

P ⊂ O