Given [ (p → q) ^ (q → r) ] ^ ( p^ ~r) 1. = [(~p v q) ^ (~q v r) ]^ (p^ ~r) 2. = [ ((~p v q) ^ ~q) v ((~p v q) ^ r)]^(p^~r) 3. = [ ((~p ^ ~q) v (q ^ ~q)) v ((~p ^ r) v (q a r)) ] ^ ( p ^ ~r) 4. = [ ((~p^ ~q) v F) v ((~p ^ r) v (q a r)) ] ^ ( p^ ~r) 5. = [(~pA~q) v (~pa r) v (q a r) ]^(p^~r) 6. = ((~p ^~q) ^ (p^ ~r)) v ((~p ^ r)^(p^~r)) v ((q a r) ^ (p^~r)) 7. = (~p^~q^p^~r) v (~p ar^p^~r) v (q a rapa~r) 8. = Fv FvF 9. = F What is the process used to obtain line 2? A) identity law B associative law implication (D) distributive law
Given [ (p → q) ^ (q → r) ] ^ ( p^ ~r) 1. = [(~p v q) ^ (~q v r) ]^ (p^ ~r) 2. = [ ((~p v q) ^ ~q) v ((~p v q) ^ r)]^(p^~r) 3. = [ ((~p ^ ~q) v (q ^ ~q)) v ((~p ^ r) v (q a r)) ] ^ ( p ^ ~r) 4. = [ ((~p^ ~q) v F) v ((~p ^ r) v (q a r)) ] ^ ( p^ ~r) 5. = [(~pA~q) v (~pa r) v (q a r) ]^(p^~r) 6. = ((~p ^~q) ^ (p^ ~r)) v ((~p ^ r)^(p^~r)) v ((q a r) ^ (p^~r)) 7. = (~p^~q^p^~r) v (~p ar^p^~r) v (q a rapa~r) 8. = Fv FvF 9. = F What is the process used to obtain line 2? A) identity law B associative law implication (D) distributive law
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
17.
![Given [ (p → q) A (q → r) ] ^ (p^ ~r)
1. = [(~p v q) ^ (~qv r)]^(p^ ~r)
2. = [ ((~p v q) A ~q) v ({~p v q) ^ r)]^(p^~r)
3. = [ ((~p ^ ~q) v (q ^ ~q)) v ((~p a r) v (q a r)) ] ^ ( p ^ ~r)
4. = [ ((~p ^ ~q) v F) v ((~p a r) v (qa r)) ] ^ ( p^ ~r)
5. = [(~p^~q) v (~p^ r) v (q A r) ] ^(p^~r)
6. = ((~p ^ ~q) ^ (p^ ~r)) v ((~p a r) ^ ( p^ ~r)) v ((q ar)^ (p^~r))
7. = (~pA~q^ p^ ~r) v (~p ar^p^~r) v (q a r ^ p^ ~r)
8. = Fv FvF
9. = F
What is the process used to obtain line 2?
A identity law
B associative law
c) implication
D distributive law](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ab3185b-0252-4eca-9549-98760475b01b%2Fdbab3a1f-6ef6-4885-a1fc-b0c5f1a452e7%2F87r8uejq_processed.png&w=3840&q=75)
Transcribed Image Text:Given [ (p → q) A (q → r) ] ^ (p^ ~r)
1. = [(~p v q) ^ (~qv r)]^(p^ ~r)
2. = [ ((~p v q) A ~q) v ({~p v q) ^ r)]^(p^~r)
3. = [ ((~p ^ ~q) v (q ^ ~q)) v ((~p a r) v (q a r)) ] ^ ( p ^ ~r)
4. = [ ((~p ^ ~q) v F) v ((~p a r) v (qa r)) ] ^ ( p^ ~r)
5. = [(~p^~q) v (~p^ r) v (q A r) ] ^(p^~r)
6. = ((~p ^ ~q) ^ (p^ ~r)) v ((~p a r) ^ ( p^ ~r)) v ((q ar)^ (p^~r))
7. = (~pA~q^ p^ ~r) v (~p ar^p^~r) v (q a r ^ p^ ~r)
8. = Fv FvF
9. = F
What is the process used to obtain line 2?
A identity law
B associative law
c) implication
D distributive law
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