Consider following two instances of relation Student and Faculty with…
2024
Consider following two instances of relation Student and Faculty with operation on these instances – (a) Student − Faculty (b) (Student ∩ Faculty) ∪ (Faculty ∩ Student) (c) (Student ∪ Faculty) − (Student ∩ Faculty) (d) Student ∩ Faculty
Which of the following relational algebra operations produce the same result?
- A.
b, c, d
- B.
b, d
- C.
a, b
- D.
b, c
- E.
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Correct answer: B
Step 1: Write relations
Student = {CS-900, IT-500, Cyber-300, ME-1000, CIVIL-2000}
Faculty = {EE-2000, ECE-5000, Cyber-300, DS-100, CIVIL-2000}
Step 2: Find common tuples (Intersection)
Compare both sets: Cyber-300 and CIVIL-2000 are present in both.
Student ∩ Faculty = {Cyber-300, CIVIL-2000}
Step 3: Evaluate (a) Student − Faculty
Remove common tuples from Student:
Result = {CS-900, IT-500, ME-1000}
Step 4: Evaluate (b) (Student ∩ Faculty) ∪ (Faculty ∩ Student)
Both intersections are same, so union remains same:
Result = {Cyber-300, CIVIL-2000}
Step 5: Evaluate (c) (Student ∪ Faculty) − (Student ∩ Faculty)
First take union (all unique tuples):
{CS-900, IT-500, Cyber-300, ME-1000, CIVIL-2000, EE-2000, ECE-5000, DS-100}
Now remove common tuples:
Result = {CS-900, IT-500, ME-1000, EE-2000, ECE-5000, DS-100}
Step 6: Evaluate (d) Student ∩ Faculty
Result = {Cyber-300, CIVIL-2000}
Conclusion: (b) and (d) give the same result, while (a) and (c) are different.