Mathematical Logic Exercise 1.7 [Page 17] Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 1

EXERCISE 1.7 [PAGE 17]

EXERCISE 1.7PAGE 17

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 1 Mathematical Logic Exercise 1.7 [Page 17]

EXERCISE 1.7Q 1.1   PAGE 17

Exercise 1.7 | Q 1.1 | Page 17

Write the dual of the following:

(p ∨ q) ∨ r

SOLUTION

(p ∧ q) ∧ r

EXERCISE 1.7Q 1.2   PAGE 17

Exercise 1.7 | Q 1.2 | Page 17

Write the dual of the following:

~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]

SOLUTION

~(p ∧ q) ∨ [p ∧ ~ (q ∨ ~ r)]

EXERCISE 1.7Q 1.3   PAGE 17

Exercise 1.7 | Q 1.3 | Page 17

Write the dual of the following:

p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r

SOLUTION

p ∧ (q ∧ r) ≡ (p ∧ q) ∧ r

EXERCISE 1.7Q 1.4   PAGE 17

Exercise 1.7 | Q 1.4 | Page 17

Write the dual of the following:

~(p ∧ q) ≡ ~ p ∨ ~ q

SOLUTION

~(p ∨ q) ≡ ~ p ∧ ~ q

EXERCISE 1.7Q 2.1   PAGE 17

Exercise 1.7 | Q 2.1 | Page 17

Write the dual statement of the following compound statement.

13 is a prime number and India is a democratic country.

SOLUTION

13 is a prime number or India is a democratic country.

EXERCISE 1.7Q 2.2   PAGE 17

Exercise 1.7 | Q 2.2 | Page 17

Write the dual statement of the following compound statement.

Karina is very good or everybody likes her.

SOLUTION

Karina is very good and everybody likes her.

EXERCISE 1.7Q 2.3   PAGE 17

Exercise 1.7 | Q 2.3 | Page 17

Write the dual statement of the following compound statement.

Radha and Sushmita cannot read Urdu.

SOLUTION

Radha or Sushmita cannot read Urdu.

EXERCISE 1.7Q 2.4   PAGE 17

Exercise 1.7 | Q 2.4 | Page 17

Write the dual statement of the following compound statement.

A number is a real number and the square of the number is non-negative.

SOLUTION

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