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(a,a) ∈ R, for every a ∈ A. This condition is for which of the following relations?
  • a)
    Reflexive relation
  • b)
    Symmetric relation
  • c)
    Equivalence relation
  • d)
    Transitive relation
Correct answer is option 'A'. Can you explain this answer?
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(a,a) ∈ R, for every a ∈ A. This condition is for which of t...
The above is the condition for a reflexive relation. A relation is said to be reflexive if every element in the set is related to itself.
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(a,a) ∈ R, for every a ∈ A. This condition is for which of t...

Reflexive relation:

- A relation R on set A is said to be reflexive if (a, a) ∈ R for every element a ∈ A.
- In other words, a relation is reflexive if every element in the set A is related to itself.
- The condition stated in the question, (a, a) ∈ R for every a ∈ A, precisely defines a reflexive relation.
- Therefore, the given condition is for a reflexive relation.

Symmetric relation:

- A relation R on set A is said to be symmetric if for every (a, b) ∈ R, (b, a) ∈ R.
- This property does not match the condition given in the question, which focuses on the diagonal elements (a, a).
- Hence, the given condition does not apply to a symmetric relation.

Equivalence relation:

- An equivalence relation is a relation that is reflexive, symmetric, and transitive.
- While the given condition aligns with the reflexive property, it does not cover the other aspects required for an equivalence relation.
- Therefore, the condition in the question does not define an equivalence relation.

Transitive relation:

- A relation R on set A is transitive if for all (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R.
- The condition given does not involve elements in the form of (a, b) and (b, c) but focuses solely on the diagonal elements (a, a).
- Thus, the condition does not pertain to a transitive relation.
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(a,a) ∈ R, for every a ∈ A. This condition is for which of the following relations?a)Reflexive relationb)Symmetric relationc)Equivalence relationd)Transitive relationCorrect answer is option 'A'. Can you explain this answer?
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