# Chapter 1: Mathematical Logic

#### EXERCISE 1.1

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

#### EXERCISE 1.1Q 1    PAGE 2

Exercise 1.1 | Q 1 | Page 2

# State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.

## A triangle has ‘n’ sides

### SOLUTION

It is an open sentence. Hence, it is not a statement.

[Note: Answer given in the textbook is ‘it is a statement’. However, we found that ‘It is not a statement’.]

#### EXERCISE 1.1Q 2    PAGE 2

Exercise 1.1 | Q 2 | Page 2

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## The sum of interior angles of a triangle is 180°

### SOLUTION

It is a statement which is true. Hence, it’s truth value is T.

#### EXERCISE 1.1Q 3    PAGE 2

Exercise 1.1 | Q 3 | Page 2

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## You are amazing!

### SOLUTION

It is an exclamatory sentence. Hence, it is not a statement.

#### EXERCISE 1.1Q 4    PAGE 2

Exercise 1.1 | Q 4 | Page 2

# State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.

## Please grant me a loan.

### SOLUTION

It is a request. Hence, it is not a statement.

#### EXERCISE 1.1Q 5    PAGE 2

Exercise 1.1 | Q 5 | Page 2

# State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.

## √-4  is an irrational number.

### SOLUTION

It is a statement which is false. Hence, it’s truth value is F.

#### EXERCISE 1.1Q 6   PAGE 2

Exercise 1.1 | Q 6 | Page 2

# State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.

## x2 − 6x + 8 = 0 implies x = −4 or x = −2.

### SOLUTION

It is a statement which is false. Hence, it’s truth value if F.

#### EXERCISE 1.1Q 7    PAGE 3

Exercise 1.1 | Q 7 | Page 3

# State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.

## He is an actor.

### SOLUTION

It is an open sentence. Hence, it is not a statement.

#### EXERCISE 1.1Q 8    PAGE 3

Exercise 1.1 | Q 8 | Page 3

# State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.

## Did you eat lunch yet?

### SOLUTION

It is an interrogative sentence. Hence, it is not a statement.

#### EXERCISE 1.1Q 9   PAGE 3

Exercise 1.1 | Q 9 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## Have a cup of cappuccino.

### SOLUTION

It is an imperative sentence, hence it is not a statement.

#### EXERCISE 1.1Q 10    PAGE 3

Exercise 1.1 | Q 10 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## (x + y)2 = x2 + 2xy + y2 for all x, y ∈ R.

### SOLUTION

It is a statement which is true. Hence, it’s truth value is T.

#### EXERCISE 1.1Q 11    PAGE 3

Exercise 1.1 | Q 11 | Page 3

# State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.

## Every real number is a complex number.

### SOLUTION

It is a statement which is true. Hence, it’s truth value is T.

#### EXERCISE 1.1Q 12   PAGE 3

Exercise 1.1 | Q 12 | Page 3

# State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.

## 1 is a prime number.

### SOLUTION

It is a statement which is false. Hence, it’s truth value is F.

#### EXERCISE 1.1Q 13   PAGE 3

Exercise 1.1 | Q 13 | Page 3

# State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.

## With the sunset the day ends.

### SOLUTION

It is a statement which is true. Hence, it’s truth value is T.

#### EXERCISE 1.1Q 14    PAGE 3

Exercise 1.1 | Q 14 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## 1 ! = 0

### SOLUTION

It is a statement which is false. Hence, it’s truth value is F.

[Note: Answer in the textbook is incorrect]

#### EXERCISE 1.1Q 15    PAGE 3

Exercise 1.1 | Q 15 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## 3 + 5 > 11

### SOLUTION

It is a statement which is false. Hence, it’s truth value is F.

#### EXERCISE 1.1Q 16   PAGE 3

Exercise 1.1 | Q 16 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## The number π is an irrational number.

### SOLUTION

It is a statement which is true. Hence, it’s truth value is T.

[Note: Answer in the textbook is incorrect]

#### EXERCISE 1.1Q 17   PAGE 3

Exercise 1.1 | Q 17 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## x2 - y2 = (x + y)(x - y) for all x, y ∈ R.

### SOLUTION

It is a statement which is true. Hence, it’s truth value is T.

#### EXERCISE 1.1Q 18    PAGE 3

Exercise 1.1 | Q 18 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## The number 2 is the only even prime number.

### SOLUTION

It is a statement which is true. Hence, it’s truth value is T.

#### EXERCISE 1.1Q 19   PAGE 3

Exercise 1.1 | Q 19 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## Two co-planar lines are either parallel or intersecting.

### SOLUTION

It is a statement which is true. Hence, it’s truth value is T.

#### EXERCISE 1.1Q 20   PAGE 3

Exercise 1.1 | Q 20 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## The number of arrangements of 7 girls in a row for a photograph is 7!.

### SOLUTION

It is a statement which is true. Hence, it’s truth value is T.

#### EXERCISE 1.1Q 21   PAGE 3

Exercise 1.1 | Q 21 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## Give me a compass box.

### SOLUTION

It is an imperative sentence. Hence, it is not a statement.

#### EXERCISE 1.1Q 22   PAGE 3

Exercise 1.1 | Q 22 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## Bring the motor car here.

### SOLUTION

It is an imperative sentence. Hence, it is not a statement.

#### EXERCISE 1.1Q 23    PAGE 3

Exercise 1.1 | Q 23 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## It may rain today.

### SOLUTION

It is an open sentence. Hence, it is not a statement.

#### EXERCISE 1.1Q 24   PAGE 3

Exercise 1.1 | Q 24 | Page 3

# State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

## If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.

### SOLUTION

It is a statement which is true. Hence, it’s truth value is T.

#### EXERCISE 1.1Q 25   PAGE 3

Exercise 1.1 | Q 25 | Page 3