Question

Assume that AB → C, C  → D and D → A are simultaneously satisfied by a relation r(R). What are the candidate keys of this relation?
1. AB, CD and AD
2. AB and CD
3. AB and DB
4. ABCD and BC

Answer 1

Correct Answer - Option 3 : AB and DB

If closure defined the complete relation then become the candidate key.

• Closure of AB =  (AB)⁺ = {A,B,C,D}         //candidate key
• Closure of BC =  (BC)+ = {A,B,C,D}        //candidate key
• Closure of CD = (CD)⁺ = {C,D,A} 
• Closure of DB = (DB)⁺= {B,C,D,A}         //candidate key
• Closure of ABCD = (ABCD)⁺= {A,B,C,D}    //super key
• Closure of AD = (AD)⁺ = {A,B,D}

The candidate keys are AB. BC, BD