1. (7 points) Verify the following logical equivalence by using logicalequivalence laws in Theorem 2.1.1.(pV ~ q) V (~ p^~g) =~ p(You should show your work.)Theorem 2.1.1 Logical EquivalencesGiven any statement variables p, q, and r, a tautology t and a contradiction c, the following logical equivalenceshold.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=ppVc=p5. Negation laws:6. Double negative law:pV ~p =t(~p) = p7. Idempotent laws:PAp pPVp=ppAc =c-(pv q) = -p A~qpA (p v q) = p8. Universal bound laws:pvt=t9. De Morgan's laws:(pAg) =-p V~q10. Absorption laws:pv (p^g) =p11. Negations oft and c:

We will prove this using the logical equivalence laws given in the question.

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

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

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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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

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:

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