Supply the reason for each step to show the equivalence of (pV ~ q) ^ (~ pV ~ q) and ~ q. ~(p V ~q) V (~p ^ ~q) = (~p ^q) V (~p^~q) Step 1. = ~pA (q V ~q) Step 2. =pAt Step 3. = mp Step 4. Therefore, (p V ~q) V (~p A ~q) = ~p.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Topic Video
Question

Write if Step 1,2,3,4 are either: Identity laws, De Morgan's law, Distributive laws, or Negation laws

Supply the reason for each step to show the equivalence of
(pV ~ q) ^ (~ pv ~ q) and ~ q.
(p V ~q) V (~p A ~q) = (~p ^q) V (~p ^ ~q) Step 1.
= ~p A (q V ~q)
Step 2.
= ~pAt
Step 3.
= ~p
Step 4.
Therefore, (p V ~q) V (~p ^ ~q) = ~p.
Transcribed Image Text:Supply the reason for each step to show the equivalence of (pV ~ q) ^ (~ pv ~ q) and ~ q. (p V ~q) V (~p A ~q) = (~p ^q) V (~p ^ ~q) Step 1. = ~p A (q V ~q) Step 2. = ~pAt Step 3. = ~p Step 4. Therefore, (p V ~q) V (~p ^ ~q) = ~p.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Propositional Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,