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In the set W of whole numbers an equivalence relation R is defined as follows :
aRb iff both a and b leave same remainder when divided by 5. The equivalence class of 1 is given by
  • a)
    {0, 5, 10, 15, ...}
  • b)
    {1, 6, 11, 16, ...}
  • c)
    {2, 7, 12, 17, ...}
  • d)
    {4, 9, 14, 19, ...}
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In the set W of whole numbers an equivalence relation R is defined as ...
Equivalence Relation R

  • aRb iff both a and b leave same remainder when divided by 5



Equivalence Class of 1

  • {1, 6, 11, 16, ...}



Explanation
An equivalence relation is a relation that satisfies three properties: reflexive, symmetric, and transitive. In this case, the relation R is defined as both a and b leaving the same remainder when divided by 5.

To find the equivalence class of 1, we need to find all the numbers that leave the same remainder as 1 when divided by 5. We can do this by adding or subtracting multiples of 5 from 1:


  • 1

  • 1 + 5 = 6

  • 1 + 10 = 11

  • 1 + 15 = 16

  • ...


Therefore, the equivalence class of 1 is {1, 6, 11, 16, ...}, which is option B.
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In the set W of whole numbers an equivalence relation R is defined as ...
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In the set W of whole numbers an equivalence relation R is defined as follows :aRb iff both a and b leave same remainder when divided by 5. The equivalence class of 1 is given bya){0, 5, 10, 15, ...}b){1, 6, 11, 16, ...}c){2, 7, 12, 17, ...}d){4, 9, 14, 19, ...}Correct answer is option 'B'. Can you explain this answer?
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