6. Let S be the set of the subsets of 2= {1,2,3, 4} . Define a relation Ron Sas follows: For X and Y in S : X RY means Xn{1,3} =Yn{1,3}. It is easy to see R is an equivalence relation on S- no need to verify that claim. Describe the equivalence classes of R by explicitly listing all the elements in each class. Note, the result of your work can be viewed as describing the partition Pof the set S, induced by the relation R.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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6. Let S be the set of the subsets of 2 = {1,2, 3, 4} . Define a relation Ron S as follows:
For X and Y in S : X RY means Xn{1,3} =Yn{1,3}. It is easy to see R is an equivalence relation
on S- no need to verify that claim. Describe the equivalence classes of R by explicitly listing all the
elements in each class. Note, the result of your work can be viewed as describing the partition Pof the
set S, induced by the relation R.
Transcribed Image Text:6. Let S be the set of the subsets of 2 = {1,2, 3, 4} . Define a relation Ron S as follows: For X and Y in S : X RY means Xn{1,3} =Yn{1,3}. It is easy to see R is an equivalence relation on S- no need to verify that claim. Describe the equivalence classes of R by explicitly listing all the elements in each class. Note, the result of your work can be viewed as describing the partition Pof the set S, induced by the relation R.
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