7. Let the propositional constants "P", “Q”, and “R” serve as atomic sentences in the formal language PL representing unspecified English sentences having no truth-functional structure. Each of (a) through (f) below is a sentence in "Loglish", a first step toward a translation from some truth-functionally complex English sentence to a molecular sentence of PL. (a) If not both P and Q, then not R. (b) R unless neither P nor Q. (c) Not P if not Q, if not R. (d) Not P, if not Q if not R. . (e) P and Q just in case not R. (f) R only if either not P or not Q. Now consider the following sentences in PL: I. (P VQ) → RII. (~P V ~Q) → ~R IV. (~R~Q) - V. (PAQ) VI. (PAQ) - VII. (~P V ~Q) → R IX. ~(PAQ) → ~R X. (~R~P) → ~Q XI. ~R→ → (~Q → ~P) XII. ~R→ → (~P→~Q) For each of the given Loglish sentences (a) – (f), choose from among the sentences I – XII in PL the one that captures best the logical structure of the Loglish sentence. Write the appropriate Roman Numerals in the blanks to the left of the corresponding Loglish sentences. III. ~R→ (PAQ) ~R → (~P V ~Q) VIII. R→ ~R NOTE: For some Loglish sentences, there might be more than one equally acceptable answer. In such a case, you need only select one acceptable answer in order to receive full credit. Also, some of I - XII might be used more than once, while some might not be used at all.
7. Let the propositional constants "P", “Q”, and “R” serve as atomic sentences in the formal language PL representing unspecified English sentences having no truth-functional structure. Each of (a) through (f) below is a sentence in "Loglish", a first step toward a translation from some truth-functionally complex English sentence to a molecular sentence of PL. (a) If not both P and Q, then not R. (b) R unless neither P nor Q. (c) Not P if not Q, if not R. (d) Not P, if not Q if not R. . (e) P and Q just in case not R. (f) R only if either not P or not Q. Now consider the following sentences in PL: I. (P VQ) → RII. (~P V ~Q) → ~R IV. (~R~Q) - V. (PAQ) VI. (PAQ) - VII. (~P V ~Q) → R IX. ~(PAQ) → ~R X. (~R~P) → ~Q XI. ~R→ → (~Q → ~P) XII. ~R→ → (~P→~Q) For each of the given Loglish sentences (a) – (f), choose from among the sentences I – XII in PL the one that captures best the logical structure of the Loglish sentence. Write the appropriate Roman Numerals in the blanks to the left of the corresponding Loglish sentences. III. ~R→ (PAQ) ~R → (~P V ~Q) VIII. R→ ~R NOTE: For some Loglish sentences, there might be more than one equally acceptable answer. In such a case, you need only select one acceptable answer in order to receive full credit. Also, some of I - XII might be used more than once, while some might not be used at all.
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
Transcribed Image Text:7. Let the propositional constants “P”, “Q”, and “R” serve as atomic sentences in the formal language PL
representing unspecified English sentences having no truth-functional structure. Each of (a) through (f) below
is a sentence in "Loglish”, a first step toward a translation from some truth-functionally complex English
sentence to a molecular sentence of PL.
(a) If not both P and Q, then not R.
(b) R unless neither P nor Q.
(c) Not P if not Q, if not R.
(d) Not P, if not Q if not R.
(e) P and Q just in case not R.
(f) R only if either not P or not Q.
Now consider the following sentences in PL:
I. (P VQ) → RII. (~P V ~Q)→ ~R
IV. (~R → ~Q) → ~P
VII. (~P V ~Q) → R
III. ~R→ (PAQ)
V. (PAQ) → R
VIII. R (~P V ~Q)
X. (~R ~P) → ~Q
XI. ~R → (~Q→ ~P)
XII. ~R (~P- ~Q)
For each of the given Loglish sentences (a) – (f), choose from among the sentences I - XII in PL the one that
best captures the logical structure of the Loglish sentence. Write the appropriate Roman Numerals in the
blanks to the left of the corresponding Loglish sentences.
VI. (P ^ Q) ↔ ~R
IX. ~(PAQ) → ~R
NOTE: For some Loglish sentences, there might be more than one equally acceptable answer. In such a case,
you need only select one acceptable answer in order to receive full credit. Also, some of I – XII might be used
more than once, while some might not be used at all.
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