Given [ (p q) n (q r)]A(~r) 1. = [(-p v q) A(~qvr)]^(p^~r) 2. = [ ((-p v q) ^ ~q) v ((~p v q) A r)]A(pA~r) 3. = [ ((-p A ~q) v (q)v (~pAnv()]A(p~r) 4. = [ ((-p^~q) v F) v ((~p Ar) v n)] r) 5. = [(-p^~q) v(~pAr) v (q A r)] A(pA~r) 6. = (~pA ~q) A(p^~r)) v ((~pAr)^(p^~r)) v ((qa ) 7. = (~p^~q ^pA~r)v (-p ArApA-r)v ( r) 8. = Fv Fv F 9. = F What is the process used to obtain line 4? A) distributive law B de Morgan's Law © identity law D complement law

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Given [ (p q) (q - r)]A (pA~r)
1. = [(-p v q)A(~qvr)]^(p^~r)
2. = [ ((-p v q) ^ ~q) v ((~p v q) An)JA(pA~r)
3. = [ ((-pA ~q) v (q A ~q)) v ((~p Ar)v (qAr) ]A(pA ~r)
4. = [ ((-p^ ~q) v F) v ((-p Ar) v (qan) ] ^ ( p^ ~r)
5. = [(-p^ ~q) v(~pAr) v (q A r)]A(p^~r)
6. = ((-p A ~q) A(p^~r)) v ((-p A r)^(p^~r)) v ((qan(r)
7. = (~p A ~q^ p^ ~r) v (~parap^ ~r) v (q Arap^~r)
8. = Fv Fv F
9. = F
What is the process used to obtain line 4?
(A) distributive law
de Morgan's Law
© identity law
(D complement law
Transcribed Image Text:Given [ (p q) (q - r)]A (pA~r) 1. = [(-p v q)A(~qvr)]^(p^~r) 2. = [ ((-p v q) ^ ~q) v ((~p v q) An)JA(pA~r) 3. = [ ((-pA ~q) v (q A ~q)) v ((~p Ar)v (qAr) ]A(pA ~r) 4. = [ ((-p^ ~q) v F) v ((-p Ar) v (qan) ] ^ ( p^ ~r) 5. = [(-p^ ~q) v(~pAr) v (q A r)]A(p^~r) 6. = ((-p A ~q) A(p^~r)) v ((-p A r)^(p^~r)) v ((qan(r) 7. = (~p A ~q^ p^ ~r) v (~parap^ ~r) v (q Arap^~r) 8. = Fv Fv F 9. = F What is the process used to obtain line 4? (A) distributive law de Morgan's Law © identity law (D complement law
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