Correct : 6

To find the total number of superkeys for the relation R(A, B, C, D), we need to use the properties of candidate keys and apply the mathematical principle of inclusion-exclusion.
1. Identify the Given Variables
The relation R has 4 total attributes: n = 4 (A, B, C, D).
Candidate Key 1 (CK₁) = {A, B}
Candidate Key 2 (CK₂) = {A, C}
2. Calculate Superkeys from CK₁
A superkey is any superset of a candidate key. To find the superkeys generated by {A, B}, we can append any combination of the remaining attributes, which are {C, D}.
There are 4 - 2 = 2 remaining attributes.
The number of superkeys generated by CK₁ is 2² = 4.
(These are: {A, B}, {A, B, C}, {A, B, D}, {A, B, C, D})
3. Calculate Superkeys from CK₂
Similarly, to find the superkeys generated by {A, C}, we can append any combination of its remaining attributes, which are {B, D}.
There are 4 - 2 = 2 remaining attributes.
The number of superkeys generated by CK₂ is 2² = 4.
(These are: {A, C}, {A, B, C}, {A, C, D}, {A, B, C, D})
4. Subtract the Common Superkeys (Intersection)
If we simply add 4 + 4, we will double-count the superkeys that contain both {A, B} and {A, C}. We must subtract this intersection.
The union of the two candidate keys is {A, B} ∪ {A, C} = {A, B, C}.
The remaining attributes not in this union: 4 - 3 = 1 attribute (which is {D}).
The number of common superkeys is 2¹ = 2.
(These are exactly {A, B, C} and {A, B, C, D})
5. Final Calculation
Total Superkeys = Superkeys(CK₁) + Superkeys(CK₂) - Common Superkeys
Total Superkeys = 4 + 4 - 2 = 6.
Correct Answer: 6