5. |The following question concerns the conjecture: If A nB sD, then A D. (a) Let P be the statement "x e A", Q be the statement "x EB", and R be the statement "x E D. Rewrite the conjecture above as a propositional logic statement using P, Q. and R. (b) The following is a proof of the conjecture above. Either verify the proof is correct, or explain why the proof is incorrect and provide a counterexample or correct proof. Assume that A n B S D, and take x E AN B. Then by the definition of intersection, x e A. Additionally, since ANBSD, we have x ED. Therefore ASD.
5. |The following question concerns the conjecture: If A nB sD, then A D. (a) Let P be the statement "x e A", Q be the statement "x EB", and R be the statement "x E D. Rewrite the conjecture above as a propositional logic statement using P, Q. and R. (b) The following is a proof of the conjecture above. Either verify the proof is correct, or explain why the proof is incorrect and provide a counterexample or correct proof. Assume that A n B S D, and take x E AN B. Then by the definition of intersection, x e A. Additionally, since ANBSD, we have x ED. Therefore ASD.
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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Transcribed Image Text:5. |The following question concerns the conjecture: If A nB sD, then A D.
(a) Let P be the statement "x e A", Q be the statement "x EB", and R be the statement "x
E D. Rewrite the conjecture above as a propositional logic statement using P, Q.
and R.
(b) The following is a proof of the conjecture above. Either verify the proof is correct, or
explain why the proof is incorrect and provide a counterexample or correct proof.
Assume that A n B S D, and take x E AN B. Then by the definition of
intersection, x e A. Additionally, since ANBSD, we have x ED. Therefore
ASD.
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