EXERCISE 1.7 [PAGE 17]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 1: Mathematical Logic

Question 1.1 | Page 17

Write the dual of the following:

\((p \lor q) \lor r\)

SOLUTION

\((p \land q) \land r\)

Question 1.2 | Page 17

Write the dual of the following:

\(\sim(p \lor q) \land [p \lor \sim (q \land \sim r)]\)

SOLUTION

\(\sim(p \land q) \lor [p \land \sim (q \lor \sim r)]\)

Question 1.3 | Page 17

Write the dual of the following:

\(p \lor (q \lor r) \equiv (p \lor q) \lor r\)

SOLUTION

\(p \land (q \land r) \equiv (p \land q) \land r\)

Question 1.4 | Page 17

Write the dual of the following:

\(\sim(p \land q) \equiv \sim p \lor \sim q\)

SOLUTION

\(\sim(p \lor q) \equiv \sim p \land \sim q\)

Question 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.

Question 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.

Question 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.

Question 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.