समुच्चय \(A=\{1,2,3\}\) पर identity relation (I_A={(1,1),(2,2),(3,3)}) है। \(I_A\) की सही प्रकृति क्या है?
On \(A=\{1,2,3\}\), the identity relation is (I_A={(1,1),(2,2),(3,3)}). What is the correct nature of \(I_A\)?
Explanation opens after your attempt
A. तुल्यता संबंध और आंशिक क्रम दोनोंBoth equivalence relation and partial order
Concept
The identity relation is reflexive, symmetric, and transitive, so it is an equivalence relation. It is also reflexive, antisymmetric, and transitive, so it is a partial order.
Why this answer is correct
The correct answer is A. तुल्यता संबंध और आंशिक क्रम दोनों / Both equivalence relation and partial order. The identity relation is reflexive, symmetric, and transitive, so it is an equivalence relation. It is also reflexive, antisymmetric, and transitive, so it is a partial order.
Exam Tip
Identity relation reflexive, symmetric और transitive है, इसलिए equivalence relation है। यह reflexive, antisymmetric और transitive भी है, इसलिए partial order भी है।
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