### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 1 Mathematical Logic Exercise 1.2 [Page 6]

#### EXERCISE 1.2Q 1.1 PAGE 6

Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5

#### SOLUTION

Let p : e is a vowel.

q : 2 + 3 = 5

The symbolic form is p ∨ q.

#### EXERCISE 1.2Q 1.2 PAGE 6

Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.

#### SOLUTION

Let p : Mango is a fruit.

q : Potato is a vegetable.

The symbolic form is p Λ q.

#### EXERCISE 1.2Q 1.3 PAGE 6

Express the following statement in symbolic form.

Milk is white or grass is green.

#### SOLUTION

Let p : Milk is white.

q : Grass is green.

The symbolic form is p ∨ q.

#### EXERCISE 1.2Q 1.4 PAGE 6

Express the following statement in symbolic form.

I like playing but not singing.

#### SOLUTION

Let p : I like playing.

q : I do not like singing.

The symbolic form is p ∧ q.

#### EXERCISE 1.2Q 1.5 PAGE 6

Express the following statement in symbolic form.

Even though it is cloudy, it is still raining.

#### SOLUTION

Let p : It is cloudy.

q : It is still raining.

The symbolic form is p ∧ q.

#### EXERCISE 1.2Q 2.1 PAGE 6

Write the truth value of the following statement.

Earth is a planet and Moon is a star.

#### SOLUTION

Let p : Earth is a planet.

q : Moon is a star.

The truth values of p and q are T and F respectively.

The given statement in symbolic form is p ∧ q.

∴ p ∧ q ≡ T ∧ F ≡ F

∴ Truth value of the given statement is F.

#### EXERCISE 1.2Q 2.2 PAGE 6

Write the truth value of the following statement.

16 is an even number and 8 is a perfect square.

#### SOLUTION

Let p : 16 is an even number.

q : 8 is a perfect square.

The truth values of p and q are T and F respectively.

The given statement in symbolic form is p ∧ q.

∴ p ∧ q ≡ T ∧ F ≡ F

∴ Truth value of the given statement is F.

#### EXERCISE 1.2Q 2.3 PAGE 6

Write the truth value of the following statement.

A quadratic equation has two distinct roots or 6 has three prime factors.

#### SOLUTION

Let p : A quadratic equation has two distinct roots.

q : 6 has three prime factors.

The truth values of p and q are F and F respectively.

The given statement in symbolic form is p ∨ q.

∴ p ∨ q ≡ F ∨ F ≡ F

∴ Truth value of the given statement is F.

#### EXERCISE 1.2Q 2.4 PAGE 6

Write the truth value of the following statement.

The Himalayas are the highest mountains but they are part of India in the North East.

#### SOLUTION

Let p : Himalayas are the highest mountains.

q : Himalayas are the part of India in the north east.

The truth values of p and q are T and T respectively.

The given statement in symbolic form is p ∧ q.

∴ p ∧ q ≡ T ∧ T ≡ T

∴ Truth value of the given statement is T.