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set theory

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{}  =  ∅, both are equal which is empty set .

{∅} : it is set which contains ∅ as elements ..

Comparison between ∅, {∅},
∅ is subset of every set that is why it is called Trivial SubSet of any set. 
so  ∅ ⊆ {∅} and ∅ ∊ {∅}.

Cardinality of ∅ is 0 and that of {∅} is 1. 

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