Let X be a set. Let P be a set of subsets of X such that: • Ø & P; the union of all sets A € Pis X. Note that these are clauses (a) and (c) of the definition of a partition (Definition 1.5). Now define a relation R on the set X by R={(x, y):x EA and ye A for some A € P}, as in Theorem 1.7(b). Which of the following is true? Select one: a. R must be reflexive and transitive but might not be symmetric. b. R must be reflexive and symmetric but might not be transitive. R must ho.cum
Let X be a set. Let P be a set of subsets of X such that: • Ø & P; the union of all sets A € Pis X. Note that these are clauses (a) and (c) of the definition of a partition (Definition 1.5). Now define a relation R on the set X by R={(x, y):x EA and ye A for some A € P}, as in Theorem 1.7(b). Which of the following is true? Select one: a. R must be reflexive and transitive but might not be symmetric. b. R must be reflexive and symmetric but might not be transitive. R must ho.cum
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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![QUESTION 8
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 (Definition 1.5).
Now define a relation R on the set X by R={(x, y):x EA and ye A for some A E P}, as in Theorem 1.7(b). Which of the following is true?
Select one:
a. R must be reflexive and transitive but might not be symmetric.
b. R must be reflexive and symmetric but might not be transitive.
C.
R must be symmetric and transitive but might not be reflexive.
d. R must be an equivalence relation, but { [x]R:XEX} might not be equal to P.
e.
R must be an equivalence relation, and {[x]R: XEX} must equal P.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9337f081-cc74-4ca5-9ca3-6c212ee96a0a%2F5d291a5c-aaa1-427c-a55f-e04a9e553362%2Frho9epi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QUESTION 8
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 (Definition 1.5).
Now define a relation R on the set X by R={(x, y):x EA and ye A for some A E P}, as in Theorem 1.7(b). Which of the following is true?
Select one:
a. R must be reflexive and transitive but might not be symmetric.
b. R must be reflexive and symmetric but might not be transitive.
C.
R must be symmetric and transitive but might not be reflexive.
d. R must be an equivalence relation, but { [x]R:XEX} might not be equal to P.
e.
R must be an equivalence relation, and {[x]R: XEX} must equal P.
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