Simplify -(-s→(-q^-s)) to ¬s^q

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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I need help with this problem, please list out the exact laws that were used.

Simplify -(-s-(-q^-s)) to -s^q
1. Select a law from the right to apply
Laws
Distributive
Complement
-(-s-(-qA-s))
(алb)v(алс)
an(bvc)
av-a
ET
(avb)A(avc)
av(bac)
an-a E F
Commutative
= F
avb
bva
F
= T
anb
ba
Identity
De Morgan's
ant E a
-(anb)
-av-b
avF E a
-(avb)
-ал-b
Double negation
Conditional
ma E a
a-b
¬avb
ab
(a-b)^(b¬a)
II
II
III
II
II
II
II
III
Transcribed Image Text:Simplify -(-s-(-q^-s)) to -s^q 1. Select a law from the right to apply Laws Distributive Complement -(-s-(-qA-s)) (алb)v(алс) an(bvc) av-a ET (avb)A(avc) av(bac) an-a E F Commutative = F avb bva F = T anb ba Identity De Morgan's ant E a -(anb) -av-b avF E a -(avb) -ал-b Double negation Conditional ma E a a-b ¬avb ab (a-b)^(b¬a) II II III II II II II III
Expert Solution
Step 1

The following laws are used to simplify the given logical expression.

  • Conditional Law: ab¬ab.
  • Double Negation Law: ¬¬aa.
  • Commutative Law: abba.
  • Redundancy Law: a¬abab.
  • De Morgan's Law: ¬ab¬a¬b.
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