Maharashtra State BoardHSC Arts 12th Board Exam
Advertisement Remove all ads

Using the rules in logic, write the negation of the following: (p ∨ q) ∧ (q ∨ ∼r) - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum

Using the rules in logic, write the negation of the following:

(p ∨ q) ∧ (q ∨ ∼r)

Advertisement Remove all ads

Solution

The negation of (p ∨ q) ∧ (q ∨ ∼r) is
∼ [(p ∨ q) ∧ (q ∨ ∼r)]
≡ ∼(p ∨ q) ∨ ∼(q ∨ ∼r) .....(Negation of conjunction)
≡ (∼p ∧ ∼q) ∨ [∼q ∧ ∼(∼r)] ...............(Negation of disjunction
≡ (∼p ∧ ∼q) ∨ (∼q ∧ r) ...........(Negation of negation)
≡ (∼q ∧ ∼p) ∨ (∼q ∧ r) ..........(Commutative law)
≡ (∼q) ∧ (∼p ∨ r) ..........(Distributive Law)

Concept: Algebra of Statements
  Is there an error in this question or solution?

APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 11.1 | Page 34
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×