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12.3. Consider the formula ³x‡yªz(P(x, y) ^ P(z, y) ^ P(x, z) ^ ¬P(z, x)). Under each of these interpretations, is this formula true? In each case, R is the relation corresponding to P. (a) U =N, R= {(x, y) : x < y}. (b) U=N, R= {(x,x+ 1) :x ≥0}. (c) U= the set of all bit strings, R = {(x, y) : x is lexicographically earlier than y}. (d) U = the set of all bit strings, R= {(x, y): y=x0 or y=x1}. (e) U=P(N), R = {(A, B) : A ≤ B}.

12.3. Consider the formula ³x‡yªz(P(x, y) ^ P(z, y) ^ P(x, z) ^ ¬P(z, x)). Under each of these interpretations, is this formula true? In each case, R is the relation corresponding to P. (a) U =N, R= {(x, y) : x < y}. (b) U=N, R= {(x,x+ 1) :x ≥0}. (c) U= the set of all bit strings, R = {(x, y) : x is lexicographically earlier than y}. (d) U = the set of all bit strings, R= {(x, y): y=x0 or y=x1}. (e) U=P(N), R = {(A, B) : A ≤ B}.

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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12.3. Consider the formula ³x³y³z (P(x, y) P(z,y) ^ P(x, z) ^ ¬P(z, x)). Under each of these interpretations, is this formula true? In each case, R is the relation corresponding to P. (a) U=N, R= {(x, y) : x < y}. (b) U=N, R={(x,x+ 1) :x ≥ 0}. (c) U= the set of all bit strings, R = {(x, y) : x is lexicographically earlier than y}. (d) U= the set of all bit strings, R = {(x, y): y=x0 or y=x1}. (e) U=P(N), R={(A, B) : ACB}.
Transcribed Image Text:12.3. Consider the formula ³x³y³z (P(x, y) P(z,y) ^ P(x, z) ^ ¬P(z, x)). Under each of these interpretations, is this formula true? In each case, R is the relation corresponding to P. (a) U=N, R= {(x, y) : x < y}. (b) U=N, R={(x,x+ 1) :x ≥ 0}. (c) U= the set of all bit strings, R = {(x, y) : x is lexicographically earlier than y}. (d) U= the set of all bit strings, R = {(x, y): y=x0 or y=x1}. (e) U=P(N), R={(A, B) : ACB}.
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