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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)
  • a)
    R is relexive and transitive
  • b)
    R is an equivalence relation
  • c)
    R is symmetric and not transitive
  • d)
    R is not relexive and not symmetric
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let R be a non-empty relation on a collection of sets defined by ARB i...
Is a subset of B.

To prove that R is an equivalence relation, we need to show that it satisfies the three properties of reflexivity, symmetry, and transitivity.

1. Reflexivity: For any set A, A is a subset of itself. Therefore, ARB is true for all sets A, which means that R is reflexive.

2. Symmetry: If A is a subset of B, then B is not necessarily a subset of A. Therefore, the relation ARB does not imply the relation BRB. This means that R is not symmetric.

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. This means that R is transitive.

Since R is reflexive and transitive, but not symmetric, it is not an equivalence relation.
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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)a)R is relexive and transitiveb)R is an equivalence relationc)R is symmetric and not transitived)R is not relexive and not symmetricCorrect answer is option 'C'. Can you explain this answer?
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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)a)R is relexive and transitiveb)R is an equivalence relationc)R is symmetric and not transitived)R is not relexive and not symmetricCorrect answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation 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 = Ø Then (pick the TRUE statement)a)R is relexive and transitiveb)R is an equivalence relationc)R is symmetric and not transitived)R is not relexive and not symmetricCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 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 = Ø Then (pick the TRUE statement)a)R is relexive and transitiveb)R is an equivalence relationc)R is symmetric and not transitived)R is not relexive and not symmetricCorrect answer is option 'C'. Can you explain this answer?.
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