Suppose the schema Widgets area brightness changeability de

Suppose the schema Widgets = {area, brightness, changeability, density, energy} has the FD\'s e->b e->a cd->e cd->a a->b a) This is not a minimal set of FD\'s. Explain. b) Display graphically a minimal set equivalent to the given set. c) How many keys are there for this set? d) List them all. e) Take one of those keys, and prove it\'s one. f) What is the highest normal form the schema is in? Explain. g) Give a scenario for an insert anomaly caused by this low NF.

Solution

e->b

e->a

cd->e

cd->a

a->b

a)This is not a minimal set of FD\'s. becuase cd->a is reduntant. if you have \'cd\' then with 3rd dependency(cd->e) you can deduce to \'e\' and via(e->a) you can deduce to \'a\'.

similary e->b is also redundant if you have \'e\' then via(e->a) you can get \'a\' and further via (a->b) you can deduce to \'b\'

b)A minimal set equivalent to the given set:

e->a

cd->e

a->b

c) Number of keys for this set: 1

d) {cd} is the minimal set of keys

e) from \'cd\' you can deduce \'e\' via (cd->e) then from \'e\' you can deduce \'a\' via (e->a) after that from \'a\' you can deduce \'b\' via(a->b) thus you have all 5 a,b,c,d,e if you have cd. Thus \'cd\' is primary key

f) 1NF:every relationship is in 1NF always.

2NF: As there is a composite primary key {cd} but individually c or d not determine any another non prime attribute that\'s why it is in 2nd NF

3NF: there is a transitive dependency as cd->e and e->a .that means one non prime attribute determines another non prime attribute this means it is not in 3NF form

the heighest normal form of the relation is 2NF.

g)An insert anomaly caused by this low NF: as e->a enery determines the value of \'a\' let consider you want to add the value of \'e\',\'a\' but you do not have information of c,d then you can not add that record