Let X be a set. Let P be a set of subsets of X such that: • ØEP; • the union of all sets A E P is X. Note that these are clauses (a) and (c) of the definition of a partition Now define a relation R on the set X by R = {(x, y) :x EA and y E A for some A EP}, as in Theorem 1.7(b). Which of the following is true? Select one: O a. R must be symmetric and transitive but might not be reflexive. O b. R must be reflexive and symmetric but might not be transitive. C. R must be an equivalence relation, and { [X]R:X EX} must equal P. O d. R must be reflexive and transitive but might not be symmetric. e. R must be an equivalence relation, but { [x]R:X EX} might not be equal to P.
Let X be a set. Let P be a set of subsets of X such that: • ØEP; • the union of all sets A E P is X. Note that these are clauses (a) and (c) of the definition of a partition Now define a relation R on the set X by R = {(x, y) :x EA and y E A for some A EP}, as in Theorem 1.7(b). Which of the following is true? Select one: O a. R must be symmetric and transitive but might not be reflexive. O b. R must be reflexive and symmetric but might not be transitive. C. R must be an equivalence relation, and { [X]R:X EX} must equal P. O d. R must be reflexive and transitive but might not be symmetric. e. R must be an equivalence relation, but { [x]R:X EX} might not be equal to P.
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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![Let X be a set. Let P be a set of subsets of X such that:
• Ø € P;
• the union of all sets A E P is X.
Note that these are clauses (a) and (c) of the definition of a partition
Now define a relation R on the set X by R = {(x, y) :x EA and y E A for some A EP}, as in Theorem 1.7(b). Which of the following is true?
Select one:
O a. R must be symmetric and transitive but might not be reflexive.
O b.
R must be reflexive and symmetric but might not be transitive.
C.
R must be an equivalence relation, and { [x]R:X EX} must equal P.
O d.
R must be reflexive and transitive but might not be symmetric.
e. R must be an equivalence relation, but { [x]R:X EX} might not be equal to P.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b4d98a6-2ed4-451a-82b3-b3630dcf9fce%2Fc9cf6a3f-bbd3-4b96-b91f-2f0b2652434d%2Fottrxg6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X be a set. Let P be a set of subsets of X such that:
• Ø € P;
• the union of all sets A E P is X.
Note that these are clauses (a) and (c) of the definition of a partition
Now define a relation R on the set X by R = {(x, y) :x EA and y E A for some A EP}, as in Theorem 1.7(b). Which of the following is true?
Select one:
O a. R must be symmetric and transitive but might not be reflexive.
O b.
R must be reflexive and symmetric but might not be transitive.
C.
R must be an equivalence relation, and { [x]R:X EX} must equal P.
O d.
R must be reflexive and transitive but might not be symmetric.
e. R must be an equivalence relation, but { [x]R:X EX} might not be equal to P.
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