Question:

Given the relation: \[ R = \{A, B, C, D, E, F, G\} \] With the following functional dependencies (FDs): \[ A \rightarrow BCEF, \quad E \rightarrow DG, \quad BC \rightarrow A \] Which of the following statements is correct?

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A candidate key is the minimal set of attributes that uniquely determine all attributes of the relation.

Updated On: Feb 15, 2025

A is the only candidate key of $ R $
A, B, C, D, E are candidate keys of $ R $
$ R $ is not in BCNF
A, B, C are the candidate keys of $ R $

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The Correct Option is D

Solution and Explanation

To determine the candidate keys, we analyze the closure of attributes using the given functional dependencies: 1. Find the closure of (A): \[ A^+ = \{A\} \cup \{B, C, E, F\} = \{A, B, C, E, F\} \] Since it does not include all attributes of $ R $, $ A $ alone is not a candidate key. 2. Find the closure of (BC): \[ BC^+ = \{B, C\} \cup \{A\} \cup \{B, C, E, F\} = \{A, B, C, E, F\} \] Again, it does not cover all attributes. 3. Find the closure of (A, B, C): \[ (A, B, C)^+ = \{A, B, C, E, F\} \cup \{D, G\} = \{A, B, C, D, E, F, G\} \] Since this set includes all attributes of $ R $, $ A, B, C $ together form a candidate key. Conclusion: The candidate keys of $ R $ are A, B, and C, making the correct answer (4) A, B, C are the candidate keys of $ R $.

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Questions Asked in GATE DA exam

Consider the following Python code snippet.

def f(a, b):
    if (a == 0):
        return b
    if (a % 2 == 1):
        return 2 * f((a - 1) / 2, b)
    return b + f(a - 1, b)

print(f(15, 10))

The value printed by the code snippet is 160 (Answer in integer).

GATE DA - 2025
Recursion

View Solution

Consider the following pseudocode.

Create empty stack S
Set x = 0, flag = 0, sum = 0
Push x onto S
while (S is not empty){
    if (flag equals 0){
        Set x = x + 1
        Push x onto S
    }
    if (x equals 8):
        Set flag = 1
    if (flag equals 1){
        x = Pop(S)
        if (x is odd):
            Pop(S)
        Set sum = sum + x
    }
}
Output sum

The value of $ sum $ output by a program executing the above pseudocode is:

GATE DA - 2025
Data Structures