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Types of Relations: Reflexive Symmetric Transitive & Equivalence Video Lecture | Mathematics (Maths) Class 12 - JEE

Q: 5. Give an example of an equivalence relation.

Ans. An example of an equivalence relation is the relation 'is congruent to' in geometry. If two geometric figures have the same shape and size, they are considered congruent. This relation is reflexive because any figure is congruent to itself, symmetric because if figure 'A' is congruent to figure 'B', then 'B' is also congruent to 'A', and transitive because if figure 'A' is congruent to 'B' and 'B' is congruent to 'C', then 'A' is also congruent to 'C'.

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FAQs on Types of Relations: Reflexive Symmetric Transitive & Equivalence Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is a reflexive relation?

Ans. A reflexive relation is a relation where every element is related to itself. In other words, for every element 'a' in the set, the relation contains the pair (a, a). For example, the relation "is equal to" is reflexive because every element is equal to itself.

2. Can a relation be both reflexive and symmetric?

Ans. Yes, a relation can be both reflexive and symmetric. Reflexivity means that every element is related to itself, while symmetry means that if 'a' is related to 'b', then 'b' is also related to 'a'. So, a relation can satisfy both properties by containing all the pairs (a, a) for reflexivity and (a, b) for symmetry.

3. What does it mean for a relation to be transitive?

Ans. Transitivity is a property of relations where if 'a' is related to 'b' and 'b' is related to 'c', then 'a' is also related to 'c'. In other words, if there is a chain of relationships, the transitive relation implies that the end elements are also related. For example, if 'x' is a parent of 'y' and 'y' is a parent of 'z', then the transitive relation implies that 'x' is also a parent of 'z'.

4. How can we determine if a relation is an equivalence relation?

Ans. To determine if a relation is an equivalence relation, we need to check three properties: reflexivity, symmetry, and transitivity. If the relation satisfies all three properties, it is an equivalence relation. Reflexivity ensures that each element is related to itself, symmetry guarantees that if 'a' is related to 'b', then 'b' is also related to 'a', and transitivity ensures that the relation follows a chain of relationships.

5. Give an example of an equivalence relation.

Ans. An example of an equivalence relation is the relation "is congruent to" in geometry. If two geometric figures have the same shape and size, they are considered congruent. This relation is reflexive because any figure is congruent to itself, symmetric because if figure 'A' is congruent to figure 'B', then 'B' is also congruent to 'A', and transitive because if figure 'A' is congruent to 'B' and 'B' is congruent to 'C', then 'A' is also congruent to 'C'.

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