1. Understanding Reflexive Relations
A relation R on a set A is said to be reflexive if every element of A is related to itself.
Mathematically, for a set A:
2. Calculating the Minimum Number of Pairs
Given that the set A has 10 elements, i.e., n(A)=10.
To be reflexive, R must contain at least the following pairs:
{(a1,a1),(a2,a2),…,(a10,a10)}
Since there are 10 such "identity" pairs, the minimum number of ordered pairs m must be:
3. Calculating the Maximum Number of Pairs
The maximum number of ordered pairs in any relation on set A is the total number of elements in the Cartesian product A×A.
n(A×A)=n(A)×n(A)=10×10=100
A relation is a subset of A×A, so the maximum value for m is:
4. Conclusion
The number of ordered pairs m for a reflexive relation must satisfy the condition:
Final Answer
The range for m is 10≤m≤100.
Correct Option: (A)
