Question
Total number of equivalence relations defined in the set is ?
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Step 1.
- Consider the relation R1 = { (a,a) }
it is reflexive ,symmetric and transitive
- similarly R2= {(b,b)} , R3= {(c,c)} are reflexive ,symmetric and transitive
Step 2.
- Also R4 = { (a,a) ,(b,b),(c,c), (a,b),(b,a)}
it is reflexive as(x,x)∈R(a,a)∈R for all x∈a,b,ca∈1,2,3
it is symmetric as (x,y)∈R=>(y,x)∈R(a,b)∈R=>(b,a)∈R for all x,y∈a,b,ca∈1,2,3
also it is transitive as (a,b)∈R,(b,a)∈R=>(a,a)∈R(1,2)∈R,(2,1)∈R=>(1,1)∈R
Step. 3
- The relation defined by R = {(a,a), (b,b) , (c,c) , (a,b), (a,c),(b,a),(b,c), (c,a),(c,b)}
is reflexive symmetric and transitive
- Thus Maximum number of equivalance relation on set
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| Question Text | Total number of equivalence relations defined in the set is ? |
| Answer Type | Text solution:1 |
| Upvotes | 150 |
