2. A = ¬{¬[(¬P → Q) ^ R] v ¬Q} ↔ (Q ^ R)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Simplify the following compound proposition using the rules of replacement. Put the rule that you use
![1.
2.
3.
5.
4. A. PV (QAR)=(PVQ)
B. PA(QVR)E(PAQ)
Double Negation
A.~(~P) E P
6.
7.
8.
Idempotence
A. PV PEP
Commutativity
A. PVQEQVP
9.
Associativity
A. PV (QVR)=(P VQ) VR
Distributivity
De Morgan's Law
A. (PVQ)E-PA-Q
Implication
A. P→QE-PVQ
Equivalence
A. P QE(P→Q) A (Q→P)
Exportation
A (PVR)
V (PAR)
A. [(PAQ)→R]=[P→(Q→R)]
Absurdity
10. A. [P→(Q A ~Q)] =~P
Contrapositive
11. A. P→Q=~Q→~P
Absorption
12. A. PA (PVQ)EP
Identity
RULES OF REPLACEMENT
PVT ET
13. A. PVF EP
PV-PET
PATEP
Β. ΙΡΛΕΞΕ
PA-PEF
B. PAPEP
B. PAQEQAP
B. PA(QAR)=(PAQ) AR
B. (PAQ)E-PV-Q
B. PV (PAQJEP
C.
~TEF
~FET](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93a9a0f4-d7be-4078-8aed-5dff0879be55%2Faeb5a86b-d8a8-4d62-a14f-d2a2b1f2a2a8%2Fnfkr5vt_processed.png&w=3840&q=75)
Transcribed Image Text:1.
2.
3.
5.
4. A. PV (QAR)=(PVQ)
B. PA(QVR)E(PAQ)
Double Negation
A.~(~P) E P
6.
7.
8.
Idempotence
A. PV PEP
Commutativity
A. PVQEQVP
9.
Associativity
A. PV (QVR)=(P VQ) VR
Distributivity
De Morgan's Law
A. (PVQ)E-PA-Q
Implication
A. P→QE-PVQ
Equivalence
A. P QE(P→Q) A (Q→P)
Exportation
A (PVR)
V (PAR)
A. [(PAQ)→R]=[P→(Q→R)]
Absurdity
10. A. [P→(Q A ~Q)] =~P
Contrapositive
11. A. P→Q=~Q→~P
Absorption
12. A. PA (PVQ)EP
Identity
RULES OF REPLACEMENT
PVT ET
13. A. PVF EP
PV-PET
PATEP
Β. ΙΡΛΕΞΕ
PA-PEF
B. PAPEP
B. PAQEQAP
B. PA(QAR)=(PAQ) AR
B. (PAQ)E-PV-Q
B. PV (PAQJEP
C.
~TEF
~FET
![2. A = ¬{¬[(¬P → Q) ^ R] v ¬Q} ↔ (Q ^ R)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93a9a0f4-d7be-4078-8aed-5dff0879be55%2Faeb5a86b-d8a8-4d62-a14f-d2a2b1f2a2a8%2Ffbx8kqo_processed.png&w=3840&q=75)
Transcribed Image Text:2. A = ¬{¬[(¬P → Q) ^ R] v ¬Q} ↔ (Q ^ R)
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