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L4 : Reflexive relations - Relations and Functions, Maths, Class 12 Video Lecture

FAQs on L4 : Reflexive relations - Relations and Functions, Maths, Class 12 Video Lecture

1. What is a reflexive relation?
Ans. A reflexive relation is a type of binary relation on a set where every element of the set is related to itself. In other words, for every element 'a' in the set, (a, a) belongs to the relation.
2. How can we determine if a relation is reflexive?
Ans. To determine if a relation is reflexive, we need to check if every element in the set is related to itself. For example, in a set {1, 2, 3}, if the relation contains (1, 1), (2, 2), and (3, 3), then it is reflexive. If any element is not related to itself, then the relation is not reflexive.
3. Can a relation be reflexive and symmetric at the same time?
Ans. Yes, a relation can be reflexive and symmetric at the same time. A relation is symmetric if for every (a, b) in the relation, (b, a) also belongs to the relation. If a relation satisfies both reflexive and symmetric properties, it is called an equivalence relation.
4. Are all relations reflexive?
Ans. No, not all relations are reflexive. A relation can be reflexive, non-reflexive, or irreflexive. A non-reflexive relation does not contain any pair where an element is related to itself, while an irreflexive relation does not allow any pair of the form (a, a) in the relation.
5. Can a relation be reflexive and anti-symmetric at the same time?
Ans. Yes, a relation can be reflexive and anti-symmetric at the same time. A relation is anti-symmetric if for every (a, b) and (b, a) in the relation, a = b. If a relation satisfies both reflexive and anti-symmetric properties, it is called a partial order relation.
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