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 

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