### Chapter 1 - Mathematical Logic [Latest edition] Balbharati solutions for Mathematics and Statistics 1 (Commerce)

Chapter 1 - Mathematical Logic [Latest edition]

Balbharati solutions for Mathematics and Statistics 1 (Commerce)

12th Standard HSC Maharashtra State Board

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

#### QUESTION

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’.]

#### QUESTION

The sum of interior angles of a triangle is 180°

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

#### QUESTION

You are amazing!

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

#### QUESTION

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

#### QUESTION

$\sqrt{-4}$ is an irrational number.

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

#### QUESTION

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

He is an actor.

#### QUESTION

Did you eat lunch yet?

#### QUESTION

Have a cup of cappuccino.

#### QUESTION

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

#### QUESTION

Every real number is a complex number.

#### QUESTION

1 is a prime number.

#### QUESTION

With the sunset the day ends.

1 ! = 0

3 + 5 > 11

#### QUESTION

The number π is an irrational number.

#### QUESTION

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

#### QUESTION

The number 2 is the only even prime number.

#### QUESTION

Two co-planar lines are either parallel or intersecting.

#### QUESTION

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

#### QUESTION

Give me a compass box.

#### QUESTION

Bring the motor car here.

#### QUESTION

It may rain today.

#### QUESTION

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

#### QUESTION

Can you speak in English?