HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
Account
It's free!

User


Login
Create free account


      Forgot password?
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution - Without using truth tabic show that ~(p v q)v(~p ∧ q) = ~p - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

Question

Without using truth tabic show that ~(p v q)v(~p ∧ q) = ~p

Solution

~(p v q)v(~p ∧ q)

≡~(p v q)v~(p ∨ ~q)                      by De Morgan's Law

≡~[(p ∨ q) ∧ (p ∨ ~q)]                    by De Morgan's Law

≡~{[(p ∨ q) ∧ p] ∨ [(p ∨ q)∧ ~q)]}   by Distributive Law

≡ ~{[p] ∨ [(p ∨ q) ∧ ~q]}               by  Absorption Law

≡ ~{[p] ∨ [(p∧ ~q) ∨ (q ∧ ~q)]}      by Distributive Law

≡~{[p] ∨ [(p ∧ ~q) ∨ F]}                by Complement Law

≡~{[p] ∨ [(p ∧ ~q)]}                     by Identity Law

≡~p ∧ (~p ∨ q)                             by De Morgan's Law

≡ ~p                                           by Absorption Law

Is there an error in this question or solution?

APPEARS IN

 2015-2016 (March) (with solutions)
Question 3.1.2 | 3 marks
Solution for question: Without using truth tabic show that ~(p v q)v(~p ∧ q) = ~p concept: null - Algebra of Statements. For the courses HSC Science (Computer Science), HSC Science (Electronics), HSC Arts, HSC Science (General)
S