Let A=[(~p^q)v ~ r]→(q^r). Construct a truth table for A. Hence find the principal conjunctive normal form (PCNF) of A. By using the same truth table, test the validity of the argument given below. a) (~ p^q)v~r qar Give a reason to support your answer.
Let A=[(~p^q)v ~ r]→(q^r). Construct a truth table for A. Hence find the principal conjunctive normal form (PCNF) of A. By using the same truth table, test the validity of the argument given below. a) (~ p^q)v~r qar Give a reason to support your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Let A=[(~ p^q)v ~ r]→(q^r). Construct a truth table for A. Hence find the
principal conjunctive normal form (PCNF) of A. By using the same truth table, test the
validity of the argument given below.
a)
(~p^q)v~r
qar
Give a reason to support your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0cdf8efb-f38e-4f5a-b266-f359a6465af1%2F8aeeda7d-7cc1-46a0-8e79-6d2615827ca2%2Fvme9rqq_processed.png&w=3840&q=75)
Transcribed Image Text:Let A=[(~ p^q)v ~ r]→(q^r). Construct a truth table for A. Hence find the
principal conjunctive normal form (PCNF) of A. By using the same truth table, test the
validity of the argument given below.
a)
(~p^q)v~r
qar
Give a reason to support your answer.
Expert Solution
Step 1
Truth table is as follows
| r | ||||||||
| T | T | T | F | F | F | F | T | T |
| T | T | F | F | T | F | T | F | F |
| T | F | T | F | F | F | F | F | T |
| T | F | F | F | T | F | T | F | F |
| F | T | T | T | F | T | T | T | T |
| F | T | F | T | T | T | T | F | F |
| F | F | T | T | F | F | F | F | T |
| F | F | F | T | T | F | T | F | F |
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