Predicate Logic in English

Please can someone help me solve these 3 questions for Predicate Logic in English?? I'm starting to lose the will to live....
a. Nobody likes Bart.
b. Every work-shy person is greedy.
c. Some females are mean


Consider a model MSimpsons = 〈U, I〉 _such that:

U = {Homer, Marge, Bart, Lisa, Maggie, Mr Burns}

I(h) = Homer
I(b) = Bart
I(a) = Maggie
I(m) = Marge
I(l) = Lisa
I(u) = Mr Burns

I(W) = the set of work-shy people in U = {Homer, Bart}
I(F) = the set of female people U = {Marge, Lisa, Maggie}
I(G) = the set of greedy people in U = {Homer}
I(M) = the set of mean people in U = {Mr Burns}

I(K) = the set of ordered pairs 〈x, y〉 _of individuals in U such that x likes y = {〈Homer, Homer〉, 〈Marge, Marge〉, 〈Bart, Bart〉, 〈Maggie, Maggie〉, 〈Homer, Marge〉, 〈Marge, Homer〉, 〈Homer, Maggie〉, 〈Marge, Lisa〉, 〈Marge, Maggie〉, 〈Maggie, Lisa〉, 〈Lisa, Maggie〉, 〈Mr Burns, Mr Burns〉}
I(D) = the set of ordered pairs 〈x, y〉 _of individuals in U such that x
despises y = {〈Homer, Homer〉, 〈Homer, Mr Burns〉, 〈Mr Burns, Homer〉, 〈Lisa, Bart〉}

Furthermore, let g(x) = Homer.


Would really appreciate help!

Is the question to say whether a,b and c are each true?

What happens to g(x) = Homer?

Yes got to prove whether true/false with the steps on how I got there, I'm not sure what relevance the "Let g(x) = Homer" has to be honest.

Okay, note that I am a maths student so challenge me if you disagree but this looks like a bit of a maths problem, hence why I replied.


So for the first one, you need to work out whether anyone likes Bart or not.

So the only relevant bit here is I(K), the sets that describe who like who.

From this, can you tell me if anyone likes Bart?

Yeah that's right, so the only set of ordered pairs with anyone that likes Bart is in fact himself so I think it does mean that it is true based on nobody else being listed as liking him it's just I have to put it into the formula which is what I'm no good at, really not keen on the maths side of it haha

Personally I would say false as Bart like Bart.
If this didn't count as 'somebody', I don't think they would include it.

So my answer to that would be false, because in I(K) there is <Bart, Bart> which means that Bart likes Bart, so somebody likes Bart.

Yeah you're right actually, purely based on him being included in the Universe of people in the model I guess he does count for liking himself.

Please can someone help me solve these 3 questions for Predicate Logic in English?? I'm starting to lose the will to live....
a. Nobody likes Bart.
b. Every work-shy person is greedy.
c. Some females are mean


Consider a model MSimpsons = 〈U, I〉 _such that:

U = {Homer, Marge, Bart, Lisa, Maggie, Mr Burns}

I(h) = Homer
I(b) = Bart
I(a) = Maggie
I(m) = Marge
I(l) = Lisa
I(u) = Mr Burns

I(W) = the set of work-shy people in U = {Homer, Bart}
I(F) = the set of female people U = {Marge, Lisa, Maggie}
I(G) = the set of greedy people in U = {Homer}
I(M) = the set of mean people in U = {Mr Burns}

I(K) = the set of ordered pairs 〈x, y〉 _of individuals in U such that x likes y = {〈Homer, Homer〉, 〈Marge, Marge〉, 〈Bart, Bart〉, 〈Maggie, Maggie〉, 〈Homer, Marge〉, 〈Marge, Homer〉, 〈Homer, Maggie〉, 〈Marge, Lisa〉, 〈Marge, Maggie〉, 〈Maggie, Lisa〉, 〈Lisa, Maggie〉, 〈Mr Burns, Mr Burns〉}
I(D) = the set of ordered pairs 〈x, y〉 _of individuals in U such that x
despises y = {〈Homer, Homer〉, 〈Homer, Mr Burns〉, 〈Mr Burns, Homer〉, 〈Lisa, Bart〉}

Furthermore, let g(x) = Homer.


Would really appreciate help!

Omg I had no idea set theory came up in English courses! Nice



(b) contains a universal quantifier, so the only way in which it could be true is if $\forall{I} \in I(G): I \in I(W)$. Can you find a counterexample to this? (Any $I(W) \notin I(G)$, or any work-shy person who is not greedy, would negate the statement as this would show that work-shy people being greedy is not a universally applicable rule, hence universal quantifier.

(c) contains an existential quantifier and so all you have to do to show that the statement is true is find some, i.e. at least one, female who is mean: $\exists I: I \in (I(M) \land I(F))$.

Nice one! You're a hero, think i've just about sussed it! Haha wish it didn't come up on English courses tbh haha!!

Let me know if you need any more help, logic is genuinely my favourite thing haha ^_^