How to Check Equivalence

In the Database Management System, we check equivalence using the idea of closure of functional dependencies.

Two FD sets F and G are equivalent if:

• Every FD in F can be derived from G
• Every FD in G can be derived from F

Practically, we verify this using closure (F⁺ and G⁺)

Step-by-Step Method

Step 1: Check F ⇒ G

We compute closure using F:

So G is derived from F

Step 2: Check G ⇒ F

Covers what F provides

Final Result

Technical Example

Given:

From F:

From G:

Conclusion:

Common Mistakes

• Checking only one direction
• Skipping closure calculation
• Assuming equivalence by appearance

Real Life Examples

1.  Different Routes

• Route 1: A → B → C
• Route 2: A → C

Same destination → Equivalent

2.  Coding Logic

• Long code vs optimized code
  Same output

3.  Study Methods

• Detailed notes vs short notes
  Same understanding