Question 52: write the argument using propositional wffs (use the statement lett

Question

Question 52: write the argument using propositional wffs (use the statement letters shown) Using propositional logic, prove the argument is valid.

If the birds are flying south and the leaves are turning, then it must be fall. Fall brings cold weather. The leaves are turning but the weather is not cold. Therefore, the birds are not flying south. B, L, F, C

B = the birds are flying south

L = the leaves are turning

F = it must be Fall

C = cold weather

[ (B ^ L) --> F ] ^ ( F --> C) ^ L ^ C' --> B'

Do I have the argument set up correctly? Can I get help solving?

1. (B ^ L) --> F hyp

2. F --> C hyp

3. L hyp

4. C' hyp

5. ( B ^ L )' v F 1, imp

Explanation / Answer

That argument you set is correct.

(B^L)-->F is true only when B is true ,L is try and F is true ..in all other conditions truth value is false .

F-->C is false only when F is true and C is false...in all other cases truth value is true.

If L and C' are also true then it implies B'.

(B^L)'vF if either B or L is false or both are false then(B^L)' is true.

It is false when B is true L is true and F is false.

It is true in all the other cases.

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