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Question
If R is the largest equivalence relation on a set A and S is any relation on A, then _____________ .
Options
R ⊂ S
S ⊂ R
R = S
none of these
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Solution
S ⊂ R
Since R is the largest equivalence relation on set A,
R ⊆ A × A
Since S is any relation on A,
S ⊂ R ⊆ A × A
So, S ⊂ R
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