Remember cardinality is always a relationship to another thing.

Max Cardinality(Cardinality) Always 1 or Many. Class A has a relationship to Package B with cardinality of one, that means at most there can be one occurance of this class in the package. The opposite could be a Package has a Max Cardnality of N, which would mean there can be N number of classes

Min Cardinality(Optionality) Simply means "required." Its always 0 or 1. 0 would mean 0 or more, 1 ore more

There are tons of good articles out there that explain this, including some that explain how to even property "diagram". Another thing you can search for is Cardinality/Optionality (OMG Terms) which explains the same thing, Optionality is "Min" Cardinality is "Max",

From http://www.databasecentral.info/FAQ.htm

Q: I can see how maximum cardinality is used when creating relationships between data tables. However, I don t see how minimal cardinality applies to database design. What am I missing?

A: You are correct in noticing that maximum cardinality is a more important characteristic of a relationship than minimum cardinality is. All minimum cardinality tells you is the minimum allowed number of rows a table must have in order for the relationship to be meaningful. For example, a basketball TEAM must have at least five PLAYERS, or it is not a basketball team. Thus the minimum cardinality on the PLAYER side is five and the minimum cardinality on the TEAM side is one.

One can argue that a person cannot be a player unless she is on a team, and thus the minimum cardinality of TEAM is mandatory. Similarly an organization cannot be a basketball team unless it has at least five players. The minimum cardinality of PLAYERS is mandatory also. One could argue in the opposite direction too. When a player quits a team, does it cease to be a team until a replacement is recruited? It cannot engage in any games, but does it cease to be a team? This is an example of the fact that each individual situation must be evaluated on its own terms. What is truth in THIS particular instance? The next time a similar situation arises, the decision might be different, due to different circumstances.

Agree with other answers, here s a slightly different view. Think in terms of optionality and multiplicity. Take an example: Person has Address.

Optionality asks: Does every Person need to have an Address? If so the relationship is unconditional - which means minimum cardinality is 1. If not, then min cardinality is 0.

Multiplicity asks: Can any given Person have more than one Address? If not, the maximum cardinality is 1. If so the maximum cardinality is >1. In most cases it s unbounded, usually denoted N or *.

Both are important. Non-optional associations make for simpler code since there s no need to test for existence before de-referencing: e.g.

a=person.address()

instead of

if (person.address !=null) {
  a=person.address()
}

Addresses are a good example of why Multiplicity is important. Too many business applications assume each person has exactly one address - and so can t cope when people have e.g. holiday homes.

It is possible to further constrain the cardinality, e.g. a car engine has between 2 and 12 cyclinders. However those constraints are often not very stable (Bugatti now offers a 16 cylinder engine). So the important questions are optionality and multiplicity.

hth.

Let s work with an example -

Students takes Class. Here both Students and Class are entities.A School may or may not have students enrolled in a particular semester. Think of a school offering courses in summer semester but no student is interested to join in. So, student s cardinality can be (0,N). But if a Class is going on means, it should have at least 1 student registered. So, its cardinality should be (1,N). So, you should check whether the entity participating in the relation is partial or total, which decides it s cardinality in the relation.

Hope it helps.

Maximum Cardinality:
1 to 1, 1 to many, many to many, many to 1

Minimum Cardinality:
Optional to Mandatory, Optional to Optional, Mandatory to Optional, Mandatory to Mandatory

To your question, what is the use of optionality in database design? : It becomes very helpful in the scenarios like the following.

When you design 2 tables with 1-to-1 relation, you will be confused to decide where (in which table) to have the foreign key. It s very easy to decide it, if you have optionality 1 for one table and 0 for the other table. The foreign key should be present in the former. There are many other uses for it as well.

Hope it helps.

Maximum Cardinality:- one-one, one-many, many-many

Minimum Cardinality:- zero or one

This link describes my answer, why it is so, what s the representation, and what it is.