Balbharati Maharashtra State Board 12th Commerce Maths Solution Book Pdf Chapter 1 Mathematical Logic Ex 1.2 Questions and Answers.

## Maharashtra State Board 12th Commerce Maths Solutions Chapter 1 Mathematical Logic Ex 1.2

Question 1.

Express the following statements in symbolic form:

(i) e is a vowel or 2 + 3 = 5.

Solution:

Let p : e is a vowel.

q: 2 + 3 = 5.

Then the symbolic form of the given statement is p ∨ q.

(ii) Mango is a fruit but potato is a vegetable.

Solution:

Let p : Mango is a fruit.

q : Potato is a vegetable.

Then the symbolic form of the given statement is p ∧ q.

(iii) Milk is white or grass is green.

Solution:

Let p : Milk is white.

q : Grass is green.

Then the symbolic form of the given statement is p ∨ q.

(iv) I like playing but not singing.

Solution:

Let p : I like playing.

q : I am not singing.

Then the symbolic form of the given statement is p ∧ q.

(v) Even though it is cloudy, it is still raining.

Solution:

The given statement is equivalent to:

It is cloudy and it is still raining.

Let p : It is cloudy.

q : It is still raining.

Then the symbolic form of the given statement is p ∧ q.

Question 2.

Write the truth values of the following statements:

(I) Earth is a planet and Moon is a star.

Solution:

Let p : Earth is a planet.

q : Moon is a star.

Then the symbolic form of the given statement is p ∧ q.

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

∴ the truth value of p ∧ q is F. …[T ∧ F ≡ F]

(ii) 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.

Then the symbolic form of the given statement is p ∧ q.

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

∴ the truth value of p ∧ q is F. ….[T ∧ F ≡ F]

(iii) 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.

Then the symbolic form of the given statement is p ∨ q.

The truth values of both p and q are F.

∴ the truth value of p ∨ q is F. …..[F ∨ F ≡ F]

(iv) The Himalayas are the highest mountains but they are part of India in the northeast.

Solution:

Let p : the Himalayas are the highest mountains.

q : They are part of India in the northeast.

Then the symbolic form of the given statement is p ∧ q.

The truth values of both p and q are T.

∴ the truth value of p ∧ q is T. …..[T ∧ T ≡ T]