## expressing sets

In the expression of sets: B={X $\in$ A:|X|<3} the expression is saying that B is a set that contains at most 3 sets X that belongs to A, right?

How do we say, B is a set that contains elements of X that belongs to A, and all X elements contains at most 3 x elements (the cardinality of X is at most 2). For example, B={{1,2},{3}}. And not, B={{1,2,3}}
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 Quote by xeon123 In the expression of sets: B={X $\in$ A:|X|<3} the expression is saying that B is a set that contains at most 3 sets X that belongs to A, right?
Assuming you meant "B is the set that consists of elements X that belong to A and which contain at most 2 elements" then: B={X $\in$ A:|X|<3}