Monadic Predicate Logic - Hard Question

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October 2nd 2011, 06:23 PM
RogueDemon

Monadic Predicate Logic - Hard Question

Symbolize the following:

Although some mean elves will bite even though not provoked, neither Bruce nor Carrie will bite unless provoked.

Symbolization attempt:

$\exists x ((Gx \wedge Hx) \wedge (Ix \wedge \neg Jx)) \wedge (\neg (Ib \vee Ic) \vee (Jb \vee Jc))$

Symbolization Key:

F{1} {1} is friendly.

G{1} {1} is mean.

H{1} {1} is an elf.

I{1} {1} will bite.

J{1} {1} is provoked.

b Bruce

c Carrie

Apparently my answer is wrong, but I don't know why. Any help would be appreciated.
October 2nd 2011, 09:42 PM
issacnewton

Re: Monadic Predicate Logic - Hard Question

whats correct answer ? is it given ? to me your answer looks fine
October 3rd 2011, 01:14 AM
emakarov

Re: Monadic Predicate Logic - Hard Question

Quote:

Originally Posted by RogueDemon

$\exists x ((Gx \wedge Hx) \wedge (Ix \wedge \neg Jx)) \wedge (\neg (Ib \vee Ic) \vee (Jb \vee Jc))$

The second part of this formula is true if Bruce was provoked, but it was Carrie who bit, while the original sentence presumably disallows this.
October 3rd 2011, 04:46 AM
issacnewton

Re: Monadic Predicate Logic - Hard Question

ahh i see

the second part should be

$(I_b \Rightarrow J_b)\wedge(I_c \Rightarrow J_c)$

right makarov ?
October 3rd 2011, 04:52 AM
emakarov

Re: Monadic Predicate Logic - Hard Question

Yes.
October 3rd 2011, 12:08 PM
RogueDemon

Re: Monadic Predicate Logic - Hard Question

Thank you! I've been stuck on this problem and another for days. :/

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