What is Equivalence?

In Database Management System, two sets of functional dependencies F and G are said to be equivalent if:

Every dependency in F can be derived from G
AND
Every dependency in G can be derived from F

In short:
Different expressions… same power.

Code Given:

Set F:

Set G:

Step 1: Check F ⇒ G

From F:

So G is derivable from F

Step 2: Check G ⇒ F

From G:

We already have everything G provides.

So both sets generate same dependencies

Therefore:

Technical Example

Given:

From F:

From G:

Both sets produce same closure

1.  Recipe Analogy

• Method 1: Step-by-step cooking
• Method 2: Shortcut cooking

Same dish → Equivalent

2.  Travel Routes

• Route 1: A → B → C
• Route 2: A → C directly

Same destination → Equivalent

3.  Coding Logic

• Code 1: Multi-step logic
• Code 2: Optimized logic

Same output → Equivalent