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What do you mean by "contained in" and "really contained in"?
Contained in; Any element of set A is an element of set B, and two sets may be equal.

Really contained in; Any element of set A is an element of set B, but the two sets are not equal.

In the case of inclusion, if it is included in the relationship between two equal sets, such as sets A={ 1, 2,3,4}, B={ 1, 2,3}, and C={ 1, 2,3,4}, then it can be said that B is really included.

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Intersection, Chinese vocabulary. The definition is that two straight lines cross each other and intersect at a point. Make friends; Be friends.

If A can deduce B, then A is a sufficient condition for B ... where A is a subset of B, that is, what belongs to A must belong to B, but what belongs to B does not necessarily belong to A. Specifically, if an element belongs to B but does not belong to A, then A is the proper subset of B; If what belongs to B also belongs to A, A and B are equal.

Necessary condition is a form of relation in mathematics. Without a, there must be no b; If there is a without B, A is the necessary condition of B, which is marked as B→A and read as "B is included in A". Mathematically speaking, if condition A can be deduced from result B, we say that A is a necessary condition for B. ..