Welcome to TDBSoverflow, Our class's own StackOverflow. Our rules:
  1. Use only meaningful and self-explanatory titles
  2. Tag your questions with meaningful keywords
  3. Use upvotes and downvotes to rate the answers
  4. When you receive a satisfying answer - Click the "V" button
Remember: you may get up to 5 bonus points to your final grade!

מבחן 2013 שאלה 2-ב

+2 votes
אם X הוא מפתח מינימאלי של Z U Y U X ,  אז X הוא גם מפתח מינימאלי של Y U X.

למה זה נכון?

יכול להיות שחלק מהערכים במפתח X  הם שם רק כדי להוביל לערכים של Z, ועכשיו שאין את Z אז יש ב X ערכים מיותרים ולכן הוא לא מינימלי..לא ככה?
asked Feb 3, 2018 by tikitak (2,970 points)

1 Answer

+2 votes
Best answer

First, it's easy to see that X is a key. We need to show it's minimal.

Let's prove by contradiction:

Assume there is a x in X s.t X-x is still a key for X U Y. (so X is not minimal)

We'll show X-x is also a key for X U Y U Z, contradicting the fact that X is a minimal key.

since X-x is a key to X U Y, in particular X-x --> X.

Since X is a key for X U Y U Z, we get X --> X U Y U Z,

And by transitivity we conclude X-x --> X U Y U Z, contradiction the fact that X is minimal key for X U Y U Z.

answered Feb 3, 2018 by Assaf (31,090 points)
selected Feb 3, 2018 by tikitak
you are the best ! :)