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A relation R defined on the set A = {1,2,3,5} as {(x, y): x+y >10: x,y ∈ A} is
- a)Empty relation
- b)Universal relation
- c)Zero relation
- d)Identity relation
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A relation R defined on the set A = {1,2,3,5} as {(x, y): x+y >10: ...
This relation R is not transitive.
To show this, we need to find a counterexample where the relation fails to hold for three elements in A.
Let's consider (1,2), (2,5), and (1,5). We know that (1,2) and (2,5) are in R, since 1 is less than 2 and 2 is less than 5. Similarly, (2,5) is in R because 2 is less than 5.
However, (1,5) is not in R since 1 is less than 5. Therefore, we have a counterexample where (1,2) and (2,5) are in R, but (1,5) is not. This shows that R is not transitive.
To show this, we need to find a counterexample where the relation fails to hold for three elements in A.
Let's consider (1,2), (2,5), and (1,5). We know that (1,2) and (2,5) are in R, since 1 is less than 2 and 2 is less than 5. Similarly, (2,5) is in R because 2 is less than 5.
However, (1,5) is not in R since 1 is less than 5. Therefore, we have a counterexample where (1,2) and (2,5) are in R, but (1,5) is not. This shows that R is not transitive.
Community Answer
A relation R defined on the set A = {1,2,3,5} as {(x, y): x+y >10: ...
(A)It is impossible to form a+b >10 in a relation.Thus,this is empty relation.You can also check it by adding.
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A relation R defined on the set A = {1,2,3,5} as {(x, y): x+y >10: x,y ∈ A} isa)Empty relationb)Universal relationc)Zero relationd)Identity relationCorrect answer is option 'A'. Can you explain this answer?
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A relation R defined on the set A = {1,2,3,5} as {(x, y): x+y >10: x,y ∈ A} isa)Empty relationb)Universal relationc)Zero relationd)Identity relationCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A relation R defined on the set A = {1,2,3,5} as {(x, y): x+y >10: x,y ∈ A} isa)Empty relationb)Universal relationc)Zero relationd)Identity relationCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A relation R defined on the set A = {1,2,3,5} as {(x, y): x+y >10: x,y ∈ A} isa)Empty relationb)Universal relationc)Zero relationd)Identity relationCorrect answer is option 'A'. Can you explain this answer?.
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