Determine if valid or invalid. Using Rules of Inference.26. If an animal is a squid, then it has tentacles. If an animal is an octopus, then it has tentacles. Therefore, if an animal is a squid, then it is an octopus. SymbolsNamesRuleGiven a statement, it is permissible to infer anydisjunction having that statement as one disjunct.1.Addition..P VQRules ofPAQ PAQ2.Qor PSimplificationSimplification either of its conjuncts separately.Inference..P..QGiven two statements, it is permissible to infer theconjunction having them as conjuncts.3.QConjunction..PAQP- QGiven a conditional, and given the antecedent of4. PModus Ponensthat same conditional, it is permissible to infer theconsequent of the same conditional.P.Given a conditional, and given the NEGATION of itsCONSEQUENT, it is permissible to infer theNEGATION of its antecedent.Given two conditionals such that the consequentof one matches the antecedent of the other, it ispermissible to infer a conditional having theUNMATCHED antecedent and the UNMATCHED5.Modus TollensP - QHypotheticalSyllogism(Transitivity)Q-R6. .. P-Rconsequent.P VQPVQDisjunctiveSylogism(Cancellation) disjuncts.Given a disjunction, and given the denial of oneof its disjuncts, it is permissible to infer the other7. -Por -Q..Q.PP - QGiven two conditionals (or a conjunction of twoconditionals) and given the disjunction of theirantecedents, it is permissible to infer thedisjunction of their consequents.8. PVRConstructiveDilemma.QVSP - QR -S9.-QV-SDestructiveDilemma..-P V -RP+QP+QGiven a biconditional, and given one side of thatsame, biconditional, it is permissible to infer theother side of that biconditional.10. РorQEquivalence.QPGiven a statement, it is permissible to infer that theRepetition11. ..PP → Q12. ..Р—(РЛQ)same statement.Absorption

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Determine if valid or invalid. Using Rules of Inference. 26. If an animal is a squid, then it has tentacles. If an animal is an octopus, then it has tentacles. Therefore, if an animal is a squid, then it is an octopus.

Determine if valid or invalid. Using Rules of Inference. 26. If an animal is a squid, then it has tentacles. If an animal is an octopus, then it has tentacles. Therefore, if an animal is a squid, then it is an octopus.

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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Question

Determine if valid or invalid. Using Rules of Inference.

26. If an animal is a squid, then it has tentacles. If an animal is an octopus, then it has tentacles. Therefore, if an animal is a squid, then it is an octopus.

Symbols
Names
Rule
Given a statement, it is permissible to infer any
disjunction having that statement as one disjunct.
1.
Addition
..P VQ
Rules of
PAQ PAQ
2.
Q
or P
Simplification
Simplification either of its conjuncts separately.
Inference
..P
..Q
Given two statements, it is permissible to infer the
conjunction having them as conjuncts.
3.
Q
Conjunction
..PAQ
P- Q
Given a conditional, and given the antecedent of
4. P
Modus Ponens
that same conditional, it is permissible to infer the
consequent of the same conditional.
P.
Given a conditional, and given the NEGATION of its
CONSEQUENT, it is permissible to infer the
NEGATION of its antecedent.
Given two conditionals such that the consequent
of one matches the antecedent of the other, it is
permissible to infer a conditional having the
UNMATCHED antecedent and the UNMATCHED
5.
Modus Tollens
P - Q
Hypothetical
Syllogism
(Transitivity)
Q-R
6. .. P-R
consequent.
P VQ
PVQ
Disjunctive
Sylogism
(Cancellation) disjuncts.
Given a disjunction, and given the denial of one
of its disjuncts, it is permissible to infer the other
7. -P
or -Q
..Q
.P
P - Q
Given two conditionals (or a conjunction of two
conditionals) and given the disjunction of their
antecedents, it is permissible to infer the
disjunction of their consequents.
8. PVR
Constructive
Dilemma
.QVS
P - Q
R -S
9.
-QV-S
Destructive
Dilemma
..-P V -R
P+Q
P+Q
Given a biconditional, and given one side of that
same, biconditional, it is permissible to infer the
other side of that biconditional.
10. Р
or
Q
Equivalence
.Q
P
Given a statement, it is permissible to infer that the
Repetition
11. ..P
P → Q
12. ..Р—(РЛQ)
same statement.
Absorption

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