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Consider the following functional dependencies for relational schema R(PQRSTU) are given:
PQ → RS,ST→ U,R → T,U → S,PT → R and T → P
Which of the following is/are false?
Note: {X}
+
contains all the attributes that can be derived.
  • a)
    {PT}
    +
    = {PRST}
  • b)
    {ST}
    +
    = {PQRSTU}
  • c)
    {QT}+ = {PQRSTU}
  • d)
    {PQ}+ = {PQRTU}
Correct answer is option 'A,B,D'. Can you explain this answer?
Most Upvoted Answer
Consider the following functional dependencies for relational schema R...
- P -> Q
- PQ -> R
- PR -> S
- QS -> T
- RT -> U

These functional dependencies can be interpreted as follows:

- P determines Q. This means that for every value of P, there is only one possible value for Q.
- The combination of P and Q determines R. This means that for every combination of values for P and Q, there is only one possible value for R.
- The combination of P and R determines S. This means that for every combination of values for P and R, there is only one possible value for S.
- The combination of Q and S determines T. This means that for every combination of values for Q and S, there is only one possible value for T.
- The combination of R and T determines U. This means that for every combination of values for R and T, there is only one possible value for U.

These functional dependencies help to define the relationships between the attributes in the relational schema R(PQRSTU) and ensure data integrity and consistency.
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Community Answer
Consider the following functional dependencies for relational schema R...
As we know,
{PT}
+
= {PTR}
Therefore, option (A) is false.
{ST}
+
= {STUPR}
Since Q is not present in {ST}
+
, so, option (B) is false.
{QT}
+
= {PQRSTU}
Therefore, option (C) is true.
{PQ}
+
= {PQRSTU}
In option (D), S is not present.
∴ It is false.
Now,
You might feel that option (D) is also correct but in question, it is already defined that it should contain all are derived attributes.
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Consider the following functional dependencies for relational schema R(PQRSTU) are given:PQ → RS,ST→ U,R → T,U → S,PT → R and T → PWhich of the following is/are false?Note: {X}+contains all the attributes that can be derived.a){PT}+ = {PRST}b){ST}+ = {PQRSTU}c){QT}+ = {PQRSTU}d){PQ}+ = {PQRTU}Correct answer is option 'A,B,D'. Can you explain this answer?
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