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Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B = Ø
Then (pick the TRUE statement)
Then (pick the TRUE statement)
- a)R is relexive and transitive
- b)R is symmetric and not transitive
- c)R is an equivalence relation
- d)R is not relexive and not symmetric
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let R be a non-empty relation on a collection of sets defined by ARB i...
The correct answer is B
Let, A={1,2,3}
B={4,5}
C={1,6,7}
now, A∩B=∅
B∩C=∅ but A∩C≠∅
Relation R is not transitive.
B={4,5}
C={1,6,7}
now, A∩B=∅
B∩C=∅ but A∩C≠∅
Relation R is not transitive.
A∩A=A
R is not reflexive.
R is not reflexive.
A∩B=B∩A
R is symmetric
R is symmetric
So,
A is false as R is not reflexive or transitive
B is true.
C is false because R is not transitive or reflexive
D is false because R is symmetric
A is false as R is not reflexive or transitive
B is true.
C is false because R is not transitive or reflexive
D is false because R is symmetric
Most Upvoted Answer
Let R be a non-empty relation on a collection of sets defined by ARB i...
Please explain the answer.
Even though I took some examples, I am not able to get to the answer.
if A = {1,2,3,4}
B = {1,4,9,16}
R= {(1,1), (2,4),(3,9), (4,16)}
R is not reflexive, not symmetric, not transitive.
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Community Answer
Let R be a non-empty relation on a collection of sets defined by ARB i...
Is a subset of B. Prove that R is a partial order.
To prove that R is a partial order, we need to show that it satisfies the following three properties:
1. Reflexivity: For any set A, A is a subset of itself. Therefore, ARB is true for A=A, and R is reflexive.
2. Antisymmetry: If A is a subset of B and B is a subset of A, then A and B are the same set. Therefore, if ARB and BRA, then A=B. Thus, R is antisymmetric.
3. Transitivity: If A is a subset of B and B is a subset of C, then A is a subset of C. Therefore, if ARB and BRC, then ARC. Thus, R is transitive.
Since R satisfies all three properties, it is a partial order.
To prove that R is a partial order, we need to show that it satisfies the following three properties:
1. Reflexivity: For any set A, A is a subset of itself. Therefore, ARB is true for A=A, and R is reflexive.
2. Antisymmetry: If A is a subset of B and B is a subset of A, then A and B are the same set. Therefore, if ARB and BRA, then A=B. Thus, R is antisymmetric.
3. Transitivity: If A is a subset of B and B is a subset of C, then A is a subset of C. Therefore, if ARB and BRC, then ARC. Thus, R is transitive.
Since R satisfies all three properties, it is a partial order.
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Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B =ØThen (pick the TRUE statement)a)R is relexive and transitiveb)R is symmetric and not transitivec)R is an equivalence relationd)R is not relexive and not symmetricCorrect answer is option 'B'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B =ØThen (pick the TRUE statement)a)R is relexive and transitiveb)R is symmetric and not transitivec)R is an equivalence relationd)R is not relexive and not symmetricCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B =ØThen (pick the TRUE statement)a)R is relexive and transitiveb)R is symmetric and not transitivec)R is an equivalence relationd)R is not relexive and not symmetricCorrect answer is option 'B'. Can you explain this answer?.
Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B =ØThen (pick the TRUE statement)a)R is relexive and transitiveb)R is symmetric and not transitivec)R is an equivalence relationd)R is not relexive and not symmetricCorrect answer is option 'B'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B =ØThen (pick the TRUE statement)a)R is relexive and transitiveb)R is symmetric and not transitivec)R is an equivalence relationd)R is not relexive and not symmetricCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B =ØThen (pick the TRUE statement)a)R is relexive and transitiveb)R is symmetric and not transitivec)R is an equivalence relationd)R is not relexive and not symmetricCorrect answer is option 'B'. Can you explain this answer?.
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