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suppose, e.g., we have the schema:Things = {ambience, brightness, coherence, dil

ID: 3776137 • Letter: S

Question

suppose, e.g., we have the schema:Things = {ambience, brightness, coherence, diligence}

Now consider the two English sentences:

a) Things of different brightness must have different ambience.

b) Things with the same coherence could still have different diligences.

These can be translated into the language of FD's as follows:

a) a->b holds.
b) c->d fails.

Take each of the following statements (don't impute any "meaning" to them, nor are the four scenarios necessarily consistent), and translate it similarly into an assertion that some FD holds or fails.

1) Things with different diligences could still have the same ambience.
2) It's impossible for things with different coherence to have the same brightness.
3) Things with different coherences must have different ambiences.
4) It's possible for things with different brightnesses and the same coherence to have the same diligence.

Explanation / Answer

1) a->b fails

2) b->c holds

3) a->c holds

4) bc->d fails

[where a = ambience , b = brightness , c= coherence , d = diligence]