Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
-(pV ~q) V (~ p^ ~ q) =~ p 2.

-(pV ~q) V (~ p^ ~ q) =~ p 2.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
1. (7 points) Verify the following logical equivalence by using logical equivalence laws in Theorem 2.1.1. (pV ~ q) V (~ p^~g) =~ p (You should show your work.) Theorem 2.1.1 Logical Equivalences Given any statement variables p, q, and r, a tautology t and a contradiction c, the following logical equivalences hold. 1. Commutative laws: (pAg) Ar=pA (qAr) pA(qvr) = (p Aq) v (par) pvq =qvp (pv q) vr=pV (q v r) pv (qAr) = (p v q)^ (pvr) 2. Associative laws: 3. Distributive laws: 4. Identity laws: pAt=p pVc=p 5. Negation laws: 6. Double negative law: pV ~p =t (~p) = p 7. Idempotent laws: PAp p PVp=p pAc =c -(pv q) = -p A~q pA (p v q) = p 8. Universal bound laws: pvt=t 9. De Morgan's laws: (pAg) =-p V~q 10. Absorption laws: pv (p^g) =p 11. Negations oft and c:
Transcribed Image Text:1. (7 points) Verify the following logical equivalence by using logical equivalence laws in Theorem 2.1.1. (pV ~ q) V (~ p^~g) =~ p (You should show your work.) Theorem 2.1.1 Logical Equivalences Given any statement variables p, q, and r, a tautology t and a contradiction c, the following logical equivalences hold. 1. Commutative laws: (pAg) Ar=pA (qAr) pA(qvr) = (p Aq) v (par) pvq =qvp (pv q) vr=pV (q v r) pv (qAr) = (p v q)^ (pvr) 2. Associative laws: 3. Distributive laws: 4. Identity laws: pAt=p pVc=p 5. Negation laws: 6. Double negative law: pV ~p =t (~p) = p 7. Idempotent laws: PAp p PVp=p pAc =c -(pv q) = -p A~q pA (p v q) = p 8. Universal bound laws: pvt=t 9. De Morgan's laws: (pAg) =-p V~q 10. Absorption laws: pv (p^g) =p 11. Negations oft and c:
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Basics of Inferential Statistics
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.
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,
SEE MORE TEXTBOOKS