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Logarithmic Function

The relation ...

Question

The relation 'is a subset of' in a set of sets is not an equivalence relation. Prove.

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Solution

Let A be a set.
$A \subset A .$ every set is a subset of itself. So, R is reflexive on A.
For any two sets A, B. If $A \subset B$ . It is not necessary that $B \subset A .$ Hence not symmetric and therefore not an equivalence relation.

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