Mathematical Logic Exercise 1.10 [Pages 22 - 27] Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 1

MATHEMATICS - EXERCISE 1.10 [PAGES 22 - 27]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board

Chapter 1: Mathematical Logic

EXERCISE 1.10 Q 1.1 PAGE 27

Represent the truth of the following statement by the Venn diagram.

Some hardworking students are obedient.

SOLUTION

Let U: The set of all students.

H: The set of all hardworking students.

O: The set of all obedient students.

The above Venn diagram represents truth of the given statement, \( H \cap O \neq \phi \).

EXERCISE 1.10 Q 1.2 PAGE 27

Represent the truth of the following statement by the Venn diagram.

No circles are polygons.

SOLUTION

Let U: The set of all closed geometrical figures in plane.

P: The set of all polygons.

C: The set of all circles.

The above Venn diagram represents truth of the given statement, \( P \cap C = \phi \).

EXERCISE 1.10 Q 1.3 PAGE 27

Represent the truth of the following statement by the Venn diagram.

All teachers are scholars and scholars are teachers.

SOLUTION

Let U: The set of all human beings.

T: The set of all teachers.

S: The set of all scholars.

The above Venn diagram represents truth of the given statement, \( T = S \).

EXERCISE 1.10 Q 1.4 PAGE 27

Represent the truth of the following statement by the Venn diagram.

If a quadrilateral is a rhombus, then it is a parallelogram.

SOLUTION

Let U: The set of all quadrilaterals.

P: The set of all parallelograms.

R: The set of all rhombuses.

The above Venn diagram represents truth of the given statement, \( R \subset P \).

EXERCISE 1.10 Q 2.1 PAGE 27

Draw a Venn diagram for the truth of the following statement.

Some share brokers are chartered accountants.

SOLUTION

Let U: The set of all human beings.

S: The set of all share brokers.

C: The set of all chartered accountants.

The above Venn diagram represents the truth of the given statement i.e., \( S \cap C \neq \phi \).

EXERCISE 1.10 Q 2.2 PAGE 27

Draw a Venn diagram for the truth of the following statement.

No wicket keeper is bowler, in a cricket team.

SOLUTION

Let U: The set of all human beings (or players in a cricket team).

W: The set of all wicket keepers.

B: The set of all bowlers.

The above Venn diagram represents the truth of the given statement i.e., \( W \cap B = \phi \).

EXERCISE 1.10 Q 3.1 PAGE 27

Represent the following statement by the Venn diagram.

Some non-resident Indians are not rich.

SOLUTION

Let U: The set of all human beings.

N: The set of all non-resident Indians.

R: The set of all rich people.

The above Venn diagram represents the truth of the given statement i.e., \( N - R \neq \phi \) (or \( N \cap R' \neq \phi \)).

EXERCISE 1.10 Q 3.2 PAGE 27

Represent the following statement by the Venn diagram.

No circle is rectangle.

SOLUTION

Let U: The set of all geometrical figures.

C: The set of all circles.

R: The set of all rectangles.

The above Venn diagram represents the truth of the given statement i.e., \( C \cap R = \phi \).

EXERCISE 1.10 Q 3.3 PAGE 27

Represent the following statement by the Venn diagram.

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

SOLUTION

Let U: The set of all real numbers (or integers).

P: The set of all prime numbers n such that n ≠ 2.

O: The set of all odd numbers.

The above Venn diagram represents the truth of the given statement i.e., \( P \subset O \).

View Full HSC Mathematics Solutions