# Multivalued Dependency (MVD) in DBMS

MVD or multivalued dependency means that for a single value of attribute ‘a’ multiple values of attribute ‘b’ exist. We write it as,

a --> --> b

It is read as: a is multi-valued dependent on b.

Suppose a person named Geeks is working on 2 projects Microsoft and Oracle and has 2 hobbies namely Reading and Music. This can be expressed in a tabular format in the following way.

Project and Hobby are multivalued attributes as they have more than one value for a single person i.e., Geeks.

**Multi Valued Dependency (MVD) :**

We can say that multivalued dependency exists if the following conditions are met.

**Conditions for MVD :**

Any attribute say **a** multiple define another attribute b; if any legal relation r(R), for all pairs of tuples t1 and t2 in r, such that,

t1[a] = t2[a]

Then there exists t3 and t4 in r such that.

t1[a] = t2[a] = t3[a] = t4[a] t1[b] = t3[b]; t2[b] = t4[b] t1 = t4; t2 = t3

Then multivalued (MVD) dependency exists.

To check the MVD in given table, we apply the conditions stated above and we check it with the values in the given table.

**Condition-1 for MVD –**

t1[a] = t2[a] = t3[a] = t4[a]

Finding from table,

t1[a] = t2[a] = t3[a] = t4[a] = Geeks

So, condition 1 is Satisfied.

**Condition-2 for MVD –**

t1[b] = t3[b] And t2[b] = t4[b]

Finding from table,

t1[b] = t3[b] = MS And t2[b] = t4[b] = Oracle

So, condition 2 is Satisfied.

**Condition-3 for MVD –**

∃c ∈ R-(a ∪ b) where R is the set of attributes in the relational table. t1 = t4 And t2=t3

Finding from table,

t1 = t4 = Reading And t2 = t3 = Music

So, condition 3 is Satisfied.

All conditions are satisfied, therefore,

a --> --> b

According to table we have got,

name --> --> project

And for,

a --> --> C

We get,

name --> --> hobby

Hence, we know that MVD exists in the above table and it can be stated by,

name --> --> project name --> --> hobby