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2. A = ¬{¬[(¬P → Q) ^ R] v ¬Q} ↔ (Q ^ R)

2. A = ¬{¬[(¬P → Q) ^ R] v ¬Q} ↔ (Q ^ R)

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
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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
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)
Transcribed Image Text:2. A = ¬{¬[(¬P → Q) ^ R] v ¬Q} ↔ (Q ^ R)
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