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Consider a binary relation type R that has a cardinality ratio of M:N the entity types involved are E1 with 2 instances  and E2 with 3 instances. Also E1 has total and E2 has partial Participation IN R.What is the minimum and maximum  number of instances of relationship type R?  

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1:  Maximum number of Instances in the Relationship set : 2 * 3 = 6

Since it is given that cardinality ratio is M:N. So, to make maximum instances in R, Just relate every instance of the E1 with every instance of the E2. So, 2*3 = 6 Instances maximum can be there in the relationship set R.

NOTE : Just In case, If You're getting confused with the "Partial Participation" and getting 2*2=4 as the maximum number of instances in R, then Remember that Partial Participation says that there "MAYBE" some entities which do not participate in any relationship in relationship set R. So, since we want relationships/instances in R to be maximum, we will relate every instance of E1 with every instance of E2. 

"A formal constraint: (min,max) where m, n are min and max number of times an entity participates in a relationship instance. For example, (0,10) means partial participation, and (1,max) means total participation."

2. Minimum number of instances in the relationship set = 2

Since it is given that E1 has TOTAL Participation in the relationship set R, So, By the definition of Total participation, each entity(or instance) must participate in at least one relationship/instance in the R. So, for Minimum number of instances in R, Just relate the two instances of E1 with some instance of E2. Which will be minimum 2 instances in R.

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