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Let X denote the set of all real-valued functions defined on Z. Define a relation -in X by f ~ g if f(0)1 g(0). Then the relation ~ is
- a)both reflexive and symmetric
- b)neither reflexive nor symmetric
- c)transitive but not reflexive
- d)neither transitive nor reflexive
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let X denote the set of all real-valued functions defined on Z. Define...
Given that X denote the set of all real valued functions defined on Z. Define a relation in X by f ~ g if f(0) ≠ g(0).
So, f(0) ≠ f(0) which fails reflexive relation.
If wetake f(x ) = 1- x
g(x) = x - l
Here , f(0) ≠ g(x) and we take h(x) = 1 - 2x
Here g(0) ≠ h(0)
But f(0)= h(0).
This fails transitive relation.
Hence, option (d) is correct.
So, f(0) ≠ f(0) which fails reflexive relation.
If wetake f(x ) = 1- x
g(x) = x - l
Here , f(0) ≠ g(x) and we take h(x) = 1 - 2x
Here g(0) ≠ h(0)
But f(0)= h(0).
This fails transitive relation.
Hence, option (d) is correct.
Most Upvoted Answer
Let X denote the set of all real-valued functions defined on Z. Define...
Given that X denote the set of all real valued functions defined on Z. Define a relation in X by f ~ g if f(0) ≠ g(0).
So, f(0) ≠ f(0) which fails reflexive relation.
If wetake f(x ) = 1- x
g(x) = x - l
Here , f(0) ≠ g(x) and we take h(x) = 1 - 2x
Here g(0) ≠ h(0)
But f(0)= h(0).
This fails transitive relation.
Hence, option (d) is correct.
So, f(0) ≠ f(0) which fails reflexive relation.
If wetake f(x ) = 1- x
g(x) = x - l
Here , f(0) ≠ g(x) and we take h(x) = 1 - 2x
Here g(0) ≠ h(0)
But f(0)= h(0).
This fails transitive relation.
Hence, option (d) is correct.
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Community Answer
Let X denote the set of all real-valued functions defined on Z. Define...
Relation ~ in X
The relation ~ is defined on the set X of all real-valued functions defined on Z (the set of integers). The relation ~ is defined as follows: f ~ g if f(0) < g(0),="" where="" f="" and="" g="" are="" functions="" in="" />
Reflexivity
A relation is reflexive if every element in the set is related to itself. In other words, for every function f in X, f ~ f. In this case, for a function f to be related to itself, we would need f(0) < f(0).="" however,="" this="" is="" not="" possible="" since="" a="" number="" cannot="" be="" less="" than="" itself.="" therefore,="" the="" relation="" ~="" is="" />not reflexive.
Symmetry
A relation is symmetric if whenever f is related to g, g is also related to f. In other words, if f ~ g, then g ~ f. In this case, if f(0) < g(0),="" it="" does="" not="" imply="" that="" g(0)="" />< f(0).="" therefore,="" the="" relation="" ~="" is="" />not symmetric.
Transitivity
A relation is transitive if whenever f is related to g and g is related to h, then f is related to h. In other words, if f ~ g and g ~ h, then f ~ h. In this case, if f(0) < g(0)="" and="" g(0)="" />< h(0),="" it="" implies="" that="" f(0)="" />< h(0).="" therefore,="" the="" relation="" ~="" is="" />transitive.
Conclusion
Based on the analysis above, we can conclude that the relation ~ is neither reflexive nor symmetric, but it is transitive. Therefore, the correct answer is option D) neither transitive nor reflexive.
The relation ~ is defined on the set X of all real-valued functions defined on Z (the set of integers). The relation ~ is defined as follows: f ~ g if f(0) < g(0),="" where="" f="" and="" g="" are="" functions="" in="" />
Reflexivity
A relation is reflexive if every element in the set is related to itself. In other words, for every function f in X, f ~ f. In this case, for a function f to be related to itself, we would need f(0) < f(0).="" however,="" this="" is="" not="" possible="" since="" a="" number="" cannot="" be="" less="" than="" itself.="" therefore,="" the="" relation="" ~="" is="" />not reflexive.
Symmetry
A relation is symmetric if whenever f is related to g, g is also related to f. In other words, if f ~ g, then g ~ f. In this case, if f(0) < g(0),="" it="" does="" not="" imply="" that="" g(0)="" />< f(0).="" therefore,="" the="" relation="" ~="" is="" />not symmetric.
Transitivity
A relation is transitive if whenever f is related to g and g is related to h, then f is related to h. In other words, if f ~ g and g ~ h, then f ~ h. In this case, if f(0) < g(0)="" and="" g(0)="" />< h(0),="" it="" implies="" that="" f(0)="" />< h(0).="" therefore,="" the="" relation="" ~="" is="" />transitive.
Conclusion
Based on the analysis above, we can conclude that the relation ~ is neither reflexive nor symmetric, but it is transitive. Therefore, the correct answer is option D) neither transitive nor reflexive.
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Let X denote the set of all real-valued functions defined on Z. Define a relation -in X by f ~ g if f(0)1g(0). Then the relation ~ isa)both reflexive and symmetricb)neither reflexive nor symmetricc)transitive but not reflexived)neither transitive nor reflexiveCorrect answer is option 'D'. Can you explain this answer?
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Let X denote the set of all real-valued functions defined on Z. Define a relation -in X by f ~ g if f(0)1g(0). Then the relation ~ isa)both reflexive and symmetricb)neither reflexive nor symmetricc)transitive but not reflexived)neither transitive nor reflexiveCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let X denote the set of all real-valued functions defined on Z. Define a relation -in X by f ~ g if f(0)1g(0). Then the relation ~ isa)both reflexive and symmetricb)neither reflexive nor symmetricc)transitive but not reflexived)neither transitive nor reflexiveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X denote the set of all real-valued functions defined on Z. Define a relation -in X by f ~ g if f(0)1g(0). Then the relation ~ isa)both reflexive and symmetricb)neither reflexive nor symmetricc)transitive but not reflexived)neither transitive nor reflexiveCorrect answer is option 'D'. Can you explain this answer?.
Let X denote the set of all real-valued functions defined on Z. Define a relation -in X by f ~ g if f(0)1g(0). Then the relation ~ isa)both reflexive and symmetricb)neither reflexive nor symmetricc)transitive but not reflexived)neither transitive nor reflexiveCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let X denote the set of all real-valued functions defined on Z. Define a relation -in X by f ~ g if f(0)1g(0). Then the relation ~ isa)both reflexive and symmetricb)neither reflexive nor symmetricc)transitive but not reflexived)neither transitive nor reflexiveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X denote the set of all real-valued functions defined on Z. Define a relation -in X by f ~ g if f(0)1g(0). Then the relation ~ isa)both reflexive and symmetricb)neither reflexive nor symmetricc)transitive but not reflexived)neither transitive nor reflexiveCorrect answer is option 'D'. Can you explain this answer?.
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