Logical Connective Puns

Here is a link to the working attempt that I have currently: https://imgur.com/a/QHBN4UD

I was filling out the truth table I realized I was evaluating things wrong somewhere. With the way I have things worked out, there is no logical operator that would make it a tautology. However I'm going to guess I'm evaluating it wrong somehow, and that if I do it correctly everything to the left of the question mark should work out to true in the first example, but for some reason I'm getting false. I'm guessing this because I have posted this in some other places and was told the operator that should go there is or. But I don't care to just here the answer. I would rather know how, so help is appreciate.

Edit: I figured it out but I'm going to leave it up as per rule whatever number

Is there a comprehensive (more or less) list of those English terms which correspond to logical connectives?

I did find one somewhere (Wikipedia, I think) but I'm quite sure it's far from exhaustive. For instance, for IMPLY it only includes implies, if... then and without... there is no. I'm imagining there are more.

Should no such list exist, is there some vaguely rigorous method of evaluating natural language terms for their correspondences to connectives?

I'm self-studying, not asking for homework. I'm reading the book Pure Maths for Beginners by Steve Warner and utterly failing to comprehend the very basics of logic. It says"

3) If Joanna has a cat, then fish have lungs.

Sentence 3 uses the logical connective “if...then.” The statement “fish have lungs” is false. We need to know whether Joanna has a cat in order to figure out the truth value of sentence 3. If Joanna does have a cat, then sentence 3 is false (“if T, then F” is always F). If Joanna does not have a cat, then sentence 3 is true (“if F, then F” is always T).

Obviously, neither component of 3 is related to the other. I don't understand the last sentence at all: '“if F, then F” is always T', isn't it F? why? All parts of the statement are false.

ELI5 please.

P iff Q ("P if and only if Q")
P xor Q ("either P or Q, but not both")
P or Q ("P and/or Q")
P if Q ("P is true if Q is true")
P implies Q ("if P, then Q")
P nand Q ("P and Q can't both be true")

Those are the only six logical connectives where the truth of one proposition depends on the truth of the other. Which means: if a proposition consists of two propositions and a connective, then it can be rewritten as either:

• Two separate propositions
• A proposition using one of the above connectives, and no negation
  For example:
  "If not P, then Q" becomes "P or Q"
  "If P, then not Q" becomes "P nand Q"
  "P wouldn't be true unless Q is also false, but even then, P still wouldn't necessarily be true" also becomes "P nand Q"
  "It can't be that P is false and Q is true" becomes "P if Q"

The LSAT authors love to throw a bunch of different sentence constructions at us to deliberately confuse us. As I read, I find that mentally translating a sentence into one of these six connectives simplifies the language of my internal monologue. It reduces the vocabulary, which helps me remember the text. And it eliminates negations -- most importantly, double negations.

Now, there are three ways of presenting one of these six types of logical statements. Each presentation has its advantages and disadvantage.

• As a logical connective, as described above. This is the concise and convenient way to speak, and it's easier to remember.
• In terms of the possibilities that it rules out. Looking at a set of impossibilities is a quick way to find out when you're wrong.
  e.g. "P or Q" rules out the possibility of "neither P nor Q", but it leaves the other three possibilities open.
• In terms of the inferences that it lets you make. Looking at a set of rules of inferences is a quick way to gain more knowledge.
  e.g. "P implies Q" lets you start with P and infer Q; or it lets you start with not-Q and infer not-P.

Knowing the impossibilities and rules of inference by heart helps me dissect logical arguments or infer things from them. Writing them down explicitly helps in logic games, but you have to know how to use them: use rules of inference to drive you forward, and use impossibilities either to restrict how far forward you go or to limit the different scenarios that you consider.

P iff Q
(2) impossibilities: P and ¬Q; ¬P and Q
(4) inferences: P → Q; Q → P; ¬P → ¬Q; ¬Q → ¬P

P xor Q
(2) impossibilitie

Looking online, there are many sources stating that there are only 16 Binary Logical Connectives. I understand that this is the correct answer, but can somebody explain why it is exactly 16 (or 2^(4))?

Thanks in Advance

Hi, quick question about basic logical connectives:

Propositions P and Q: P: it is hot outside. Q: it is sunny.

I'm trying to figure out how to write, "it is hot outside but not sunny." Is it P ^ ¬Q or just P¬Q?

Also, "it is not hot outside and it is not sunny." Is it ¬P ^ ¬Q?

My professor didn't give us examples past easy stuff like just ¬P, so I don't know if it is allowed to have to connectives next to each other. Thanks.

I took introductory logic over a decade ago and always wondered about this. I understand that any statement can be expressed using just AND and NOT, but when looking at truth tables, you can see that there are 16 possible logical connectives. Do we have a symbol and name for all of them?

I've searched the internet for a complete table of all symbols, but all I can turn up is the standard ^, v, ->, etc.

If this information is at all helpful in honing in on a decent answer, the reason I'm asking is because I'm writing a computer program that treats the list of possible connectives as an enumerated type (in the sense of an enum variable, not enumerable set), with the goal of writing a basic API for dealing with logical propositions and truth. Representing the connectives this way will make my code more elegant.

In case there is any confusion, this is the concept I'm talking about when referring to functional completeness:

https://en.wikipedia.org/wiki/Functional_completeness

Let p and q be the propositions p : It is below freezing. q : It is snowing.

It is either snowing or below freezing (or both).

my answer was: (p V q) V (p ^ q) but i don't get why this is wrong :(

This answer in the book was : (p V q)

This is a pretty elegant diagram of the 16 possible binary connectives: https://commons.wikimedia.org/wiki/File:Logical-connectives.gif

In fact there are a lot of other interesting logical diagrams out there if you search for them. For example, here is a modal hexagon of opposition: http://cahiers.kingston.ac.uk/images/diagram.syn10.7.6.gif

This is like the square of opposition (http://cahiers.kingston.ac.uk/images/diagram.syn10.7.2.gif). The black arrows are implication. Red lines are contradictories. Blue lines are contraries. Green lines are sub-contraries. The last two diagrams are from this page: http://cahiers.kingston.ac.uk/synopses/syn10.7.html

Interesting stuff for any of you who share a visual bent in their appreciation of logic.

http://imgur.com/a/1TDPj At the moment for question i) I have ∀xƎx D(x) --- r(x, Jin), but im not really sure what i am suppose to put in the "---", thats of course if the rest of my equation is correct. For ii) I have put ∀x~Ǝx D(x) --- r(x, Deb) which again Im not sure what to put in the place of the "---" in my equation. Im not sure if Im even half right in my equations. Any help is appreciated, Thanks!! Edit: Spelling

But also hey hope you don’t mind most of your check to go towards military spending which war is a whole other US business. Goddammit I need refuge I did not sign up to be in this fucked country .

I'm trying to connect my Arturia Keylab 99MK2 as a controller surface. I have the KeyLab connected via USB to my computer and I'm able to successfully record MIDI with it, no problem. Using Logic Pro 10.7.2 on Monterey 12.0.1

However, when attempting to setup the Keylab as a controller surface, I follow all of the provided instructions. I install the Mackie Control, and when I go into the inspector, I'm supposed to choose the KeyLab DAW as both the INPUT and the OUTPUT.

The DAW OUT is available, but it only shows MDI in. It should be also showing DAW In.

If I choose MIDI in, I'm no longer able to record MIDI from the Keystation.

See screenshot of setup - any clue why the "DAW IN" is not avail on the controller Input Port?

As you can see below, I can choose Keylab DAW for the output, but only Keylab MIDI for the input (I don't even have a mIDI cable connected to the KeyLab, only the USB)

https://preview.redd.it/hzetnhithvb81.png?width=5120&format=png&auto=webp&s=c4d36520bb67d3557712298ca727cde808258330

I recently got an Akai MPD218 pad controller, and the first time I used it I had no problem creating a software instrument track receiving signal from the device and getting sound right away when I hit the pads. However, for some reason I'm suddenly having this problem where no sound is generated when I hit the pads (the pads light up on the controller tho) and the software instruments in Logic only work with the keyboard typing feature. I'm confused because I know that Logic recognizes the MIDI controller in some way. I'll just try to list the information I'm gathering:

1. When I go to create a software instrument track, the Akai isn't listed as a device, but I believe it had been previously (when it was working last week)
2. The midi controller is highlighted in apple's MIDI Studio, so my laptop recognizes that it's connected
3. In Logic, whenever I hit a pad, the little "MIDI In" dot at the top of the screen next to the time signature/project settings lights up
4. The Akai is not listed when I go to Logic Pro > Preferences > Audio > Devices, BUT it is listed when I go to Logic Pro > Preferences > MIDI > Inputs, and I have the box next to it checked. But when I'm creating a midi track it's not listed as a device to select in the new track window.
5. I don't get any signal when I hit the pads, but when I hit record, instead of showing typical MIDI data, it records the pad numbers and displays them where you'd typically see normal midi data, like the notes and their duration.
6. I don't really understand the Environment window, but in it, Logic recognizes the device under Clicks & Ports. When I hit the pads, again, no sound comes out, but the Channel & Pad # are displayed in the "Input view" box. However, when I click on the keyboard notes displayed, I hear sound and it displays the note I just hit in the input view box.

I feel like I've tried everything I can think of but this is my first midi controller so I'm not really used to navigating it. If anyone could give me any ideas I would really appreciate it because I've spent hours trying to figure this out and it seems like the issue just came out of nowhere !!

I've tried multiple different routes to try and troubleshoot this problem but I can't seem to figure it out. I unplugged and replugged my mic, restarted my computer, etc. and nothing. I'm using a yeti mic, I've used it before with no issues but it's just not connecting for some reason. It lets me record but the line is blank.

Does anyone use their MacBook and Logic for backing tracks when playing live? I’m thinking about playing some open mics nearby and wanted to see what the best way to get the backing tracks to play through the PA would be.

When I connect my digitakt via overbridge to logic the sample in the first slot switches to reverse, it detunes to -12 and the level goes down. Even when I reload the pattern it happens again. It's only with this trigger and only when connected to logic, it's fine the rest of the time.

Anyone have something similar happen or know a fix?

Cheers!