Prime and Non Prime Attributes in DBMS with Example –
- Prime Attributes – Attribute set that belongs to any candidate key are called Prime Attributes.
(union of all the candidate key attribute)
{CK1 ∪ CK2 ∪ CK3 ∪ ……}
If Prime attribute determined by other attribute set, then more than one candidate key is possible. For example,
If A is Candidate Key, and X→A, then, X is also Candidate Key . - Non Prime Attribute – Attribute set does not belongs to any candidate key are called Non Prime Attributes.
Some Questions Based on Prime Attributes and Non Prime Attributes –
Question 1 : Given a relation R(ABCDEF) having FDs {AB→C, C→D, D→E, F→B, E→F} Identify the prime attributes and non prime attributes.
Solution : (AB)+ : {ABCDEF} ⇒ Super Key (A)+ : {A} ⇒ Not Super Key (B)+ : {B} ⇒ Not Super Key Prime Attributes : {A,B} (AB) → Candidate Key ↓ (as F → B) (AF)+ : {AFBCDE} (A)+ : {A} ⇒ Not Super key (F)+ : {FB} ⇒ Not Super Key (AF) → Candidate Key ↓ (AE)+ : {AEFBCD} (A)+ : {A} ⇒ Not Super key (E)+ : {EFB} ⇒ Not Super key (AE) → Candidate Key ↓ (AD)+ : {ADEFBC} (A)+ : {A} ⇒ Not Super key (D)+ : {DEFB} ⇒ Not Super key (AD) → Candidate Key ↓ (AC)+ : {ACDEFB} (A)+ : {A} ⇒ Not Super Key (C)+ : {DCEFB} ⇒ Not Super Key ⇒ Candidate Keys {AB, AF, AE, AD, AC} ⇒ Prime Attributes {A,B,C,D,E,F} ⇒ Non Prime Attributes {}
Question 2: Given a relation R(ABCDEF) having FDs {AB → C, C → DE, E → F, C → B} Identify the prime attributes and non prime attributes.
Solution : (AB)+ : {A B C D E F} (A)+ : {A} (B)+ : {B} (AB) ⇒ (AC), (AC)+ : {ABCDEF} (C)+ : {DECBF} ⇒ Candidate Keys {AB, AC} ⇒ Prime Attributes {A,B,C} ⇒ Non Prime Attributes {D,E,F}
Question 3: Given a relation R(ABCDEFGHIJ) having FDs {AB → C, A → DE, B → F, F → GH, D → IJ} Identify the prime attributes and non prime attributes.
Solution : (AB)+ : {ABCDEFGHIJ} (A)+ : {DEIJA} (B)+ : {FGHB} ⇒ Candidate Keys {AB} ⇒ Prime Attributes {A,B} ⇒ Non Prime Attributes {C,D,E,F,G,H,I,J}
Question 4: Given a relation R(ABDLPT) having FDs {B → PT, A → D, T → L} Identify the prime attributes and non prime attributes.
Solution : (AB)+ : {ABPTDL} (A)+ : {DA} (B)+ : {BPTL} ⇒ Candidate Keys {AB} ⇒ Prime Attributes {A,B} ⇒ Non Prime Attributes {D,L,P,T}
Question 5: Given a relation R(ABCDEFGH) having FDs {E → G, AB → C, AC → B, AD → E,B → D, BC → A} Identify the prime attributes and non prime attributes.
Solution : (ABFH)+ : {ABCDEFGH} (A)+ : {A} (B)+ : {BD} (F)+ : {F} (H)+ : {H} (AB) : {ABCDEG} (AF) : {AF} (AH) : {AH} (BF) : {BFD} (BH) : {BHD} (FH) : {FH} (ABF) : {ABFCDEG} (ABH) : {ABHCDEG} (AFH) : {AFH} (BFH) : {BDFH} None of the proper sets of {ABFH} will determine all the attributes. So {ABFH} ⇒ minimal super key or candidate key (A B FH) ↓ (A (AC) FH) ⇒ (ACFH) ( A BFH) ↓ ((BC) BFH) ⇒ (BCFH) ⇒ Candidate Keys {ABFH, ACFH, BCFH} ⇒ Prime Attributes {A,B,C,F,H} ⇒ Non Prime Attributes {D,E,G}
Question 6 :
Given a relation R(ABCDE) having FDs
{A → BC, CD → E, B → D, E → A}
Identify the prime attributes and non prime attributes.
Solution : (A)+ : {ABCDE} ⇒ (Candidate Key) (E)+ : {ABCDE} ⇒ (Candidate Key) ⇒ Candidate Keys {A,E} ⇒ Prime Attributes {A,E} ⇒ Non Prime Attributes {B,C,D}
Question 7 :
Consider a relation scheme R(ABCDEH) on which the following Functional Dependencies hold:
{A → B, BC → D, E → C, D → A}.
What are the candidate keys of R and identify the prime attributes and non prime attributes.
Solution : (BEH)+ : {BEHCDA} ⇒ Super Key (B)+ : {B} (E)+ : {EC} (H)+ : {H} (BE)+ : {BECDA} (BH)+ : {BHD} (EH)+ : {EHC} None of the proper sets of {BEH} will determine all the attributes. So, {BEH} ⇒ minimal super key or candidate key. (B EH) ↑ (A EH) ↑ (D EH) ⇒ Candidate Keys {BEH, AEH, DEH} ⇒ Prime Attributes {A,B,D,E,H} ⇒ Non Prime Attributes {C}
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