Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the relation scheme R = {E, F, G, H,...
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Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, M} and the set of functional dependencies {{E, F} -> {G}, {F} -> {I, J}, {E, H} -> {K, L}, K -> {M}, L -> {N} on R. What is the key for R?
- a){E, F}
- b){E, F, H}
- c){E, F, H, K, L}
- d){E}
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, M} and th...
All attributes can be derived from {E, F, H} To solve these kind of questions that are frequently asked in GATE paper, try to solve it by using shortcuts so that enough amount of time can be saved.
Fist Method: Using the given options try to obtain closure of each options. The solution is the one that contains R and also minimal Super Key, i.e Candidate Key.
Fist Method: Using the given options try to obtain closure of each options. The solution is the one that contains R and also minimal Super Key, i.e Candidate Key.
A) {EF}+ = {EFGIJ} ≠ R(The given relation)
B) {EFH}+ = {EFGHIJKLMN} = R (Correct since each member of the given relation is determined)
C) {EFHKL}+ = {EFGHIJKLMN} = R (Not correct although each member of the given relation can be determined but it is not minimal, since by the definition of Candidate key it should be minimal Super Key)
D) {E}+ = {E} ≠ R
B) {EFH}+ = {EFGHIJKLMN} = R (Correct since each member of the given relation is determined)
C) {EFHKL}+ = {EFGHIJKLMN} = R (Not correct although each member of the given relation can be determined but it is not minimal, since by the definition of Candidate key it should be minimal Super Key)
D) {E}+ = {E} ≠ R
Second Method:
Since, {EFGHIJKLMN}+ = {EFGHIJKLMN}
{EFGHIJKLM}+ = {EFGHIJKLMN} (Since L -> {N}, hence can replace N by L)
In a similar way K -> {M} hence replace M by K
{EFGHIJKL}+ = {EFGHIJKLMN}
Again {EFGHIJ}+ = {EFGHIJKLMN} (Since {E, H} -> {K, L}, hence replace KL by EH)
{EFGH}+ = {EFGHIJKLMN} (Since {F} -> {I, J})
{EFH}+ = {EFGHIJKLMN} (Since {E, F} -> {G})
{EFGHIJKLM}+ = {EFGHIJKLMN} (Since L -> {N}, hence can replace N by L)
In a similar way K -> {M} hence replace M by K
{EFGHIJKL}+ = {EFGHIJKLMN}
Again {EFGHIJ}+ = {EFGHIJKLMN} (Since {E, H} -> {K, L}, hence replace KL by EH)
{EFGH}+ = {EFGHIJKLMN} (Since {F} -> {I, J})
{EFH}+ = {EFGHIJKLMN} (Since {E, F} -> {G})
Most Upvoted Answer
Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, M} and th...
Explanation:
Answer: The key for R is {E, F, H}. Therefore, option 'B' is the correct answer.
- Finding the closure of each attribute:
- Closure of E: E+ = E
- Closure of F: F+ = F -> {F, I, J}
- Closure of G: G+ = G
- Closure of H: H+ = H -> {H, K, L, N, M}
- Closure of I: I+ = I
- Closure of J: J+ = J
- Closure of K: K+ = K -> {K, L, N, M}
- Closure of L: L+ = L -> {L, N, M}
- Closure of M: M+ = M
- Closure of N: N+ = N
- Finding the superkeys:
- Since {E, F} -> {G} and {F} -> {I, J}, we can combine them to get {E, F} -> {G, I, J}
- Similarly, {E, H} -> {K, L, N, M}
- Therefore, the possible superkeys are {E, F, G, I, J}, {E, H, K, L, N, M}
- Finding the candidate key:
- Since both superkeys have all the attributes of R, they are both candidate keys
- However, {E, F, H} is the minimal superkey, as removing any attribute from it would make it not a superkey anymore
- Therefore, {E, F, H} is the candidate key for R
Answer: The key for R is {E, F, H}. Therefore, option 'B' is the correct answer.
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Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, M} and the set of functional dependencies {{E, F} -> {G}, {F} -> {I, J}, {E, H} -> {K, L}, K -> {M}, L -> {N} on R. What is the key for R?a){E, F}b){E, F, H}c){E, F, H, K, L}d){E}Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, M} and the set of functional dependencies {{E, F} -> {G}, {F} -> {I, J}, {E, H} -> {K, L}, K -> {M}, L -> {N} on R. What is the key for R?a){E, F}b){E, F, H}c){E, F, H, K, L}d){E}Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, M} and the set of functional dependencies {{E, F} -> {G}, {F} -> {I, J}, {E, H} -> {K, L}, K -> {M}, L -> {N} on R. What is the key for R?a){E, F}b){E, F, H}c){E, F, H, K, L}d){E}Correct answer is option 'B'. Can you explain this answer?.
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