15% Translate the following set of sentences into formulas in first-order logic.

Question

15% Translate the following set of sentences into formulas in first-order logic. 1. Every elephant whose all children can fly is happy. 2. Every elephant dragon ean fly. 3. Every elephant who has a green child is green. You may introduce and use suitable predicates in your swers. For instance, you can use elephant (x) to say that is a elephant, green (X) to say that X is green child(C,P) to say that C is a child of P, canFly() to say that X can fly, and so on Use the resolution technique to prove or disprove that we can derive the statement: every green elephanis happ" from the above set of sentences.

Explanation / Answer

Premises:
1.For all x For all y(elephant(x) and child(y,x) and canfly(y)-->Happy(x))
2.For all x(ED(x) -->canfly(x))

   ElephantDragon(x) is elephant dragon

3. For all x There exist y(elephabt(x) and Child(x,y) and Green(y)--->G(x))
    
The conclusion is not true.

   For all x(Elephant(x) and Green(x) ---> Happy(x))

Resolving 1 and 2 does not give us any clause. Similarly we 1 and 3 also give
no clause and same with 2 & 3. As we are not getting any conclusing clause by resolving
any set of prdicagtes we can safetly say the conclusion does not hold.

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