Balbharati Maharashtra State Board 12th Commerce Maths Solution Book Pdf Chapter 1 Mathematical Logic Ex 1.1 Questions and Answers.

## Maharashtra State Board 12th Commerce Maths Solutions Chapter 1 Mathematical Logic Ex 1.1

State which of the following sentences are statements. Justify your answer. In case of statements, write down the truth value:

Question (i).

A triangle has ‘ n’ sides.

Solution:

It is a statement that is false, hence its truth value is ‘F’.

Question (ii).

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

Solution:

It is a statement that is true, hence its truth value is ‘T’.

Question (iii).

You are amazing!

Solution:

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

Question (iv).

Please grant me a loan.

Solution:

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

Question (v).

√-4 is an irrational number.

Solution:

It is a statement that is false, hence its truth value is ‘F’.

Question (vi).

x^{2} – 6x + 8 = 0 implies x = -4 or x = -2.

Solution:

It is a statement that is false, hence its truth value is ‘F’.

Question (vii).

He is an actor.

Solution:

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

Question (viii).

Did you eat lunch yet?

Solution:

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

Question (ix).

Have a cup of cappuccino.

Solution:

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

Question (x).

(x + y)^{2} = x^{2} + 2xy + y^{2} for all x, y ∈ R.

Solution:

It is a mathematical identity that is true, hence its truth value is ‘T’.

Question (xi).

Every real number is a complex number.

Solution:

It is a statement that is true, hence its truth value is ‘T.

Question (xii).

1 is a prime number.

Solution:

It is a statement that is false, hence its truth value is ‘F’.

Question (xiii).

With the sunset, the day ends.

Solution:

It is a statement that is true, hence its truth value is ‘T’.

Question (xiv).

1! = 0.

Solution:

It is a statement that is false, hence its truth value is

Question (xv).

3 + 5 > 11.

Solution:

It is a statement that is false, hence its truth value is ‘F’.

Question (xvi).

The number π is an irrational number.

Solution:

It is a statement that is true, hence its truth value is ‘T’.

Question (xvii).

x^{2} – y^{2} = (x + y)(x – y) for all x, y ∈ R.

Solution:

It is a mathematical identity that is true, hence its truth value is ‘T’.

Question (xviii).

The number 2 is only even a prime number.

Solution:

It is a statement that is true, hence its truth value is ‘T’.

Question (xix).

Two coplanar lines are either parallel or intersecting.

Solution:

It is a statement that is true, hence its truth value is ‘T’.

Question (xx).

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

Solution:

It is a statement that is true, hence its truth value is ‘T’.

Question (xxi).

Give me a compass box.

Solution:

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

Question (xxii).

Bring the motor car here.

Solution:

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

Question (xxiii).

It may rain today.

Solution:

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

Question (xxiv).

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

Solution:

It is a statement that is true, hence its truth value is ‘T’.

Question (xxv).

Can you speak English?

Solution:

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