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Determine the characteristics of the relation aRb if a2 = b2.
- a)Transitive and symmetric
- b)Reflexive and asymmetry
- c)Trichotomy, antisymmetry, and irreflexive
- d)Symmetric, Reflexive, and transitive
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Determine the characteristics of the relation aRb if a2= b2.a)Transiti...
Since, x2 = y2 is just a special case of equality, so all properties that apply to x = y also apply to this case. Hence, the relation satisfies symmetric, reflexive and transitive closure.
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Determine the characteristics of the relation aRb if a2= b2.a)Transiti...
Characteristics of the relation aRb if a^2 = b^2:
To determine the characteristics of the relation aRb where a^2 = b^2, we need to analyze the properties of the relation based on the given condition.
Symmetric:
- A relation is symmetric if for every (a, b) that belongs to the relation, (b, a) also belongs to the relation.
- In this case, if a^2 = b^2, then b^2 = a^2. Therefore, the relation is symmetric as it satisfies the condition.
Reflexive:
- A relation is reflexive if for every element 'a' in the set, (a, a) belongs to the relation.
- In this case, a^2 = a^2 is true for every element 'a' in the set. Therefore, the relation is reflexive as it satisfies the condition.
Transitive:
- A relation is transitive if for every (a, b) and (b, c) that belongs to the relation, (a, c) also belongs to the relation.
- In this case, if a^2 = b^2 and b^2 = c^2, then a^2 = c^2. Therefore, the relation is transitive as it satisfies the condition.
Therefore, the relation aRb if a^2 = b^2 is symmetric, reflexive, and transitive, which corresponds to option 'D' in the given choices.
To determine the characteristics of the relation aRb where a^2 = b^2, we need to analyze the properties of the relation based on the given condition.
Symmetric:
- A relation is symmetric if for every (a, b) that belongs to the relation, (b, a) also belongs to the relation.
- In this case, if a^2 = b^2, then b^2 = a^2. Therefore, the relation is symmetric as it satisfies the condition.
Reflexive:
- A relation is reflexive if for every element 'a' in the set, (a, a) belongs to the relation.
- In this case, a^2 = a^2 is true for every element 'a' in the set. Therefore, the relation is reflexive as it satisfies the condition.
Transitive:
- A relation is transitive if for every (a, b) and (b, c) that belongs to the relation, (a, c) also belongs to the relation.
- In this case, if a^2 = b^2 and b^2 = c^2, then a^2 = c^2. Therefore, the relation is transitive as it satisfies the condition.
Therefore, the relation aRb if a^2 = b^2 is symmetric, reflexive, and transitive, which corresponds to option 'D' in the given choices.
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