# sentence

1. ### The negation of this sentence is false

I can't tell if the logic problem "The negation of this sentence is false" is a statement or not. If the statement is initially true, then the negation would be false. If the statement is initially false, then the negation would be true. So I thought it wouldn't be a statement because...
2. ### What does "space" refer to in this sentence (from wikipedia article on gradients)?

"In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase. In simple terms, the variation in space of any quantity can be represented (e.g. graphically) by...
3. ### Applying compactness theorem in First Order Logic

Hey! Sorry for posting again so quickly, but I also have an issue for a second concept. This one is regarding applying the compactness theorem in first order logic, the framework is a Hilbert system: L is a FOL (First order language) with R, where R is a single binary predicate symbol...
4. ### number sequence vs number sentence

In the material I'm studying, it says the following; 1. A number sequence is when addition is written horizontally. 2. A number sentence is when subtraction and multiplication are written horizontally. Is this really specific to addition, subtraction and multiplication, or can they all be...
5. ### First Order Logic: Why is this sentence valid?

Let φ(x) and ψ be first order formulas so that x is not free in ψ. Show why this sentence is valid: ( (∀xφ(x) )→ ψ) ↔ (∃x( φ(x) → ψ) ) I hope someone can give me a simple semantical explanation (no need to show a natural deduction) :)
6. ### testing (sentence)

\mbox{Galois is a brilliant mathematician. Watson Come Here Mary had a little lamb}\\\mbox{JJ Thompson}\\\mbox{8 electrons in Oxygen}\\\mbox{Calculate the integral for this function:}
7. ### FOL satisfiability of a sentence

Hi Everyone! I've been revising for my exams and got stuck at this question: I would think it's E as I can't really find a model which would satisfy this sentence, though the answer is D. Could you please give me a hint as how I should approach this? Assuming that D is the correct answer I must...
8. ### Concluding sentence of a" proof by mathematical induction"-problem.

Question: What do I write in the conclusion (last statement) of a proof by mathematical induction? (first year of college level) Something including n=1, p(k), p(k+1) and P(n) i think... but I am not sure how the structure of the sentence should be.(Headbang) I need help on this! Also, do...
9. ### How to show that a given sentence is not a logical consequence of the given sentences

If I am given 4 sentences: a) ... b) ... c) ... d) ... and a conclusion f) ... How can I show that f) is not a logical consequence of a), b), c) and d) ?
10. ### Maximal consistent sets are complete

I'm stuck on a problem on the theory of structures and essentially boiled it down to this: If \Gamma is a maximal consistent set of sentences (\forall \phi \in \text{Sent}(\mathcal{L}), \Gamma \vdash \phi or \Gamma \vdash \neg \phi, but not both) is complete (\forall \phi \in...
11. ### How to make sentence with spacing

How to make sentence with spacing as below. Im using the $Latex$ style to get latex simbol or equation tq for your advice
12. ### Help with logic sentence

Here is the question: If God is Almighty, then God have the power to make a mighty stone, so God can't lift that stone. Is the sentence correct? I think it's wrong but I'm not sure.
13. ### Negation of a sentence

I need to write the negation for each of the following. I've written out what I think it should be, but was hoping someone could check. I want to be sure I understand this. \forall x \in Z, x < 0 Negation: \exists x \in Z, x \not< 0 \exists x \in Z, x = x + 1 Negation: \forall x \in Z, x...
14. ### Simple negation of sentence

All the participants of this course are IT majors or are math majors. The question asks to use basic logic laws.. and I am a bit confused on how to approach. Isn't it just Not all of the participants in this course are IT Majors or Math majors? or am I way off base?
15. ### Logical representation of sentence

Hi, I have to represent the following sentences in logic. 1. Juliet loves Romeo, her father and her mother. 2. Romeo loves Juliet and also everybody loved by Juliet. Lets say we have the predicate .loves. and the function theFatherOf. and theMotherOf. Would this be a correct...
16. ### Re-write this sentence in logical notation

"You can fool all of the people some of the time, and you can fool some of the people all of the time, but you can't fool all of the people all of the time" How do I rewrite this in logical notation? The next question is which statement is true: the original one or its negation? I don't know...
17. ### I need formal proof to a sentence

can someone give the proof to this: a*a + ab + b*b > 0 for a =/= 0 , b=/= 0. thanks
18. ### Converting Sentence to Boolean Expression...

Hey guys, If I have three variables: X, Y, and Z, and I want to convert "exactly two of the three variables" into a boolean expression, would I express that as... (X^Y^!Z) \/ (X^!Y^Z) \/ (!X^Y^Z) ...with ^ being AND, \/ being OR, and ! being NOT?
19. ### how can u place a sentence in the middle

i am using WinEdt making .tex file. how can u place a (sentence/table/matrix) in the (middle/left/right)
20. ### true,false or an open sentence

5x=28:confused: