Balbharati Maharashtra State Board 12th Commerce Maths Solution Book Pdf Chapter 1 Mathematical Logic Ex 1.7 Questions and Answers.

## Maharashtra State Board 12th Commerce Maths Solutions Chapter 1 Mathematical Logic Ex 1.7

Question 1.

Write the dual of each of the following:

(i) (p ∨ q) ∨ r

Solution:

(p ∧ q) ∧ r

(ii) ~(p ∨ q) ∧ [p ∨ ~(q ∧ ~r)]

Solution:

~(p ∧ q) ∨ [p ∧ ~(q ∨ ~r)]

(iii) p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r

Solution:

p ∧ (q ∧ r) ≡ (p ∧ q) ∧ r

(iv) ~(p ∧ q) ≡ ~p ∨ ~q

Solution:

~(p ∨ q) ≡ ~p ∧ ~q

Question 2.

Write the dual statement of each of the following compound statements:

(i) 13 is prime number and India is a democratic country.

Solution:

13 is prime number or India is a democratic country.

(ii) Karina is very good or everybody likes her.

Solution:

Karina is very good and everybody likes her.

(iii) Radha and Sushmita can not read Urdu.

Solution:

Radha or Sushmita can not read Urdu.

(iv) A number is real number and the square of the number is non-negative.

Solution:

A number is real number or the square of the number is non-negative.