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.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 16CT: Let P represent any statement. Classify as true or false. a P and P b P or P
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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.
Transcribed Image Text: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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