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See first of all we have to understand that relationship set cardinality will be defined by that entity where you are able to merge the relationship set.

As in the above ER diagram , E1 is many to one relationship with each of the remaining entities E, E3 and E4.As we know in case of one to many or many to one scenario , we merge the relationship set into that entity set which is in "many" set of the relation.The side where the arrow is shown is actually the "one side of the relationship set R.

Hence cardinality of R is also defined by E1 since it is in "many side" of the relation and hence we can merge the relationship R with E1 here.

Hence the maximum cardinality possible if all the E1 are distinct since each instance of E1 will map with atmost one of E2 , E3 and E4(follows from the definition of many to one)

Alternatively , we can also understand this like :

The primary key of a relationship in case of many to one relationship is governed by the "many side" of the relationship set i.e. primary key of relationship in this case will be primary key of the entity which is in the "many" side.

So maximum no of relationship = maximum no of distinct entries possible for an entity in the "many" side = 50.

So maximum possible entries in R = no of elements in E1   =  50

Hence 50 should be the correct answer.

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