If R = {(a,b) ∈ A × A : a = b}, what is R called?
Answer and explanation
Correct answer: Identity relation
The condition a = b allows exactly those ordered pairs whose first and second components are the same. Thus R = {(a,a) : a ∈ A}, which is the identity relation on A, commonly denoted by I_A. It contains every diagonal pair and no off-diagonal pair. It is therefore reflexive, because every element is related to itself, and it is also symmetric and transitive; however, the question asks for its name, not merely one of its properties. The universal relation would contain every pair in A × A, whereas the empty relation contains none. An inverse relation is obtained by reversing pairs of a given relation and is not the definition used here. Hence option C is correct.
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What is the correct answer to this question?
Identity relation
Why is this the correct answer?
The condition a = b allows exactly those ordered pairs whose first and second components are the same. Thus R = {(a,a) : a ∈ A}, which is the identity relation on A, commonly denoted by I_A. It contains every diagonal pair and no off-diagonal pair. It is therefore reflexive, because every element is related to itself, and it is also symmetric and transitive; however, the question asks for its name, not merely one of its properties. The universal relation would contain every pair in A × A, whereas the empty relation contains none. An inverse relation is obtained by reversing pairs of a given relation and is not the definition used here. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
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