Need help dealing with these logic sentences in First Order Form and Conjunctive

Question

Need help dealing with these logic sentences in First Order Form and Conjunctive Normal Form.

Consider the following sentences:

Blossom, Bubbles and Buttercup are members of the Girls Coding Club.

Every member of the Girls Coding Club is either a Linux-user or a Windows-user or both.

No Linux-user likes Microsoft.

All Windows-users like MSWord.

Buttercup dislikes whatever Blossom likes and likes whatever Blossom dislikes.

Blossom likes Microsoft and MSWord.

The questions to develop the sentences:

Translate these sentences into First Order Logic (FOL) sentences. Use predicates member(x), likes(x,y),Linux(x), Windows(x). Try to keep encoding as simple as possible.

Convert those sentences from First Order Logic into Conjunctive Normal Form (CNF).

Use resolution to answer the question "Is there a member of the Girls Coding Club who is a Linux-user and not a Windows-user?"

Explanation / Answer

FOL Sentences:

1.Blossom, Bubble and Buttercup are menbers of Girls Coding Club

member(Blossom) and member(Bubble) and member(Buttercup)

2. For all x (member(x) ---->Linux(x) or Windows(x) or (Linux(x) and Windows(x))

3. For all x(Linux(x)--->not likes(x,Microsoft)
4. Far all x (Windows(x)-->likes(x,MSWord)

5. For all x (Likes(Buttercup,x)--->Not Likes(Blossom,x))
   For all x (Not Likes(Buttercup,x)---->Likes(Blossom,x))

6. Likes(Blossom,Microsoft) and Likes(Blossom, MSWord)

"Is there a member of the Girls Coding Club who is a Linux-user and not a Windows-user?"

Yes it is true.It can be concluded from the second statement that there exist
member(x) such that Linux(x) holds or Windows(x) holds.

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.