Translate the following sentences into logical statements using the mentioned pr

Question

Translate the following sentences into logical statements using the mentioned predicate functions and qualifieres. Construct a derivation that corresponding to the arguments. If a conclusion does not follow, write CDNF, otherwise show the inference rules used.

1. Some scientist subjects are not interesting, but all scientific subjects are edifying. Therefore some ).

2. All thoughts are short and detached fro each other. There is not one of these thoughts which does not contain some great principles or some edifying truth. Therefore all great principles are contained in short thoughts.

Jim, George and Sue belong to an outdorr club. Every club member is either a skier or a mountain climber, but no member is both. No mountain climber likes rain, and all skiers like snow. George dislikes whateer Jim likes and likes whatever Sue dislikes. Sue dislikes. Jim and Sue both liek ran and snow. Is there a member of the outdoor club who is a mountain climber?

Explanation / Answer

1. Some scientist subjects are not interesting, but all scientific subjects are edifying. Therefore some

Some scientist subjects are not interesting
Negation: NO SCIENTIST SUBJECTS ARE INTERESTINGS
I.e., if it is false that some SCIENTISTS ARE INTERESTING, then no SCIENTIST ARE INTERESTING.

¬xP(x) x¬P(x)
¬xP(x) x¬P(x)

aLL SCIENTIFIC SUBJECTS ARE EDIFYING AND SOME

x P(x) asserts P(x) is true for every x in the domain.

x P(x) asserts P(x) is true for some x in the domain

2. All thoughts are short and detached fro each other. There is not one of these thoughts which does not contain some great principles or some edifying truth. Therefore all great principles are contained in short thoughts.

All thoughts are short and detached fro each other :

For all x, P(x)

x P(x) asserts P(x) is true for every x in the domain.

There is not one of these thoughts which does not contain some great principles or some edifying truth:

~Ax[T(x) --> A[P(x)]

T(x) = x thoughts
P(x) = x principles

x(P(x) V Q(x))

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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