Hmmm, yeah. I tried creating a truth table where everything is false and I got this using my method:
I ended up getting everything true. Oof. Ok.
Yeah that makes sense. Since while and(x,y) will make F F false, it would make T T true.
Ok. I came back to it a bit later because while I recognize that there’s an error in my method my mind is kind of stuck on it. I spent ~30 more minutes thinking about it and I’m still just kind of stuck with my previous method.
Any hints?
Describe in English what you’re trying to do, why, how you’re handling rows where you want a T output, why, how you’re handling rows where you want an F output, why.
Hmm.
I’m trying to come up with a step-by-step process in which you can create any truth table you want using “and”, “or”, and “not”. Specifically, I’m trying to come up with a method to get any combination of outputs you want on a truth table.
Depending on which output I want for the row I try to come up with a specific expression that will give me the output I want just for that row. For example, if the row is T F and I want a false output. I would come up with an expression that creates a false output. In this case, and(x,y) would work. I then combine each expression for each row using the “or” operators. In my head this is logically working out to saying: run this expression or this expression or this expression or this expression. It would then proceed to put out the output I want for each line from each expression.
I"ve come to realize that an issue with this method is that while it may produce an output that I want for one row. The same inputs are being run through a different part of the expression that could produce a different output.
So how do you create an expression that is true if and only if one specific set of inputs is provided?
How do you create an expression which is false when a specific set of inputs is provided? What result should it give for other inputs?
Do you need help with something? Are you busy? Stuck?
Mmm. Usually when I don’t post for a few a days its a mixture of being stuck and busy. It’s primarily busyness. However, sometimes when I’m busy if the assignment I’m working on is easy enough I can usually get a response posted. If it’s something thats taking me a bit more thought, I just usually wait until I’m no longer busy.
Oh yeah. To clarify: when I’m busy it’s almost always just long work days which leave me too tired to do philosophy (or anything else for that matter).
On a related note that I felt like sharing: a good amount of improvements have come about with a lot of finances and stuff at home. I have a little bit of debt I need to pay down and I want to save a bit more cash, but I can finally comfortably afford to not work as much. Come September, I have it set up with my manager to step down from my position at work and cut back my hours, so I can spend more time on philosophy/school.
Have you tried doing philosophy before work? I know there are reasons that might not work well like if work starts too early in the morning or you get too tired towards the end of your shift that way.
Mmmm. How do I create an expression that is true if and only if one specific set of inputs is provided?
(~(~x∧~y))∧(~(~x∧y))∧(~(x∧~y))∧(~(x∧y))
I came up with the above expression using the following inputs for a two-input truth table: TT, TF, FT, FF. The expression above is false for all the preceding inputs. However, if you wanted a specific set of inputs to be true you can just remove a “not (~)” from the part of the expression that corresponds with that set-of inputs.
(~x∧~y) is true for FF.
(~x∧y) is true for FT.
(x∧~y) is true for TF.
(x∧y) is true for TT.
So if I wanted an expression where only TF is true. I would have:
(~(~x∧~y))∧(~(~x∧y))∧((x∧~y))∧(~(x∧y)).
The above expression is saying that its its false when both inputs are false, false when x is false but y is true, true when x is true but y is false, and false when x and y are true.
Using the above expression I tried something similar to my previous method where I would just remove the “not” for each part of the expression to get the truth table I wanted.
It didn’t work. I realized it’s because if I removed two “nots”, for example:
(~(~x∧~y))∧((~x∧y))∧(~(x∧~y))∧((x∧y))
The resulting truth table was all false. Which makes sense since I’m saying that the inputs have to both be “false then true” and “true and true” for the expression to be true.
I did get a working method for getting any truth table I want. Take the following expression:
(~(~x∧~y))∧(~(~x∧y))∧(~(x∧~y))∧(~(x∧y))
and remove the “not” from the set of inputs you want to be true.
If you want multiple sets of inputs to be true, you would “or” multiple of the above expression. For example if you wanted a truth table that went F T F T. You would do:
(~(~x∧~y))∧((~x∧y))∧(~(x∧~y))∧(~(x∧y))∨(~(~x∧~y))∧(~(~x∧y))∧(~(x∧~y))∧((x∧y)).
So I think I’ve found a working method. Is this wrong? Is there a simpler method?
You’re overcomplicating this in some way. I was trying to ask relatively simple questions to guide you.
Say the inputs you want to be true are x=1, y=0 and you want an expression that is only true for those inputs.
Then the expression you need is: x & !y
That’s an example of how to answer this:
So how do you create an expression that is true if and only if one specific set of inputs is provided?
It doesn’t explain the general method.
Does that make sense and do you see why that expression would be true if and only if the specific inputs are provided?
Yeah, that’s typically what I try and aim for. I typically work closing shifts from 12 to 8 (though my new manager hates consistent scheduling).
Mmm. Most of my work skills are automized. So doing stuff before is not an issue.
I’d say the reason this typically doesn’t work out is bad life management that I’ve mentioned elsewhere. Which leads me to sleeping in and not having time to do stuff. If things go as I intend I try and be in bed around ~10, asleep around ~11, and wake up at 7.
Oh yeah. To clarify: when I have trouble doing philosophy after work its almost always after working all day. From something like 7am to 8pm. I’m usually too tired after these days. I have done philosophy work after working the morning/mid-day shift before.
Are you unable to fall asleep for an hour or do you do other stuff in bed besides try to sleep?
Yeah. I have a (probably?) bad habit of assuming something and then acting on it. So I thought I knew what you were getting at and worked out an answer from there. instead of just answering the question directly and waiting for more instruction.
It also didn’t help that while I don’t have time to post I do read/re-read posts on here when I get a chance so I do spend a bit of time thinking on it consciously/subconsciously before actually posting leading to me doing more than needed.
I wrote yes initially but now that I think about it. Hmm. x = 1, y = 0. x&!y. I understand why it would be true only for that set of specific inputs. Since its saying x needs to be true and y needs to be false. Other sets of inputs would be false.
Huh. I think I realized what was wrong with my first method, but I’ll wait for now before I say more.
I am able to fall asleep within that hour. If I’m having a day where everything is going well and stuff I usually fall asleep within 10 minutes it feels like.
The issues are: doing stuff in bed like watching videos or reading before I actually try and sleep or, what happens most of the time, I don’t go to bed on time as intended.
I guess to add here, I’d say its more being consistent that I struggle with in my life. I can have individual days go well, or multiple days in a row go well. Its keeping things going well over a longer period of time where I say I have bad life management.
I think sleep cycle is important. There are a lot of tips you can find for it. One is: don’t do things in bed other than sleep. If you aren’t going to sleep yet, don’t get in bed.
(x & !y) . Right?
11 = 0 & 1 = 0
10 = 1 & 1 = 1
01 = 0 & 0 = 0
00 = 0 & 1 = 0
Yeah. It’s more so being consistent/actually doing the stuff I need to do. I only go to my bed to sleep, in a sense. It’s just I use my phone as an alarm so I end up just watching a quick video or something. I know I could either just set my alarm and put my phone away from bed or just use a separate alarm . The problem is being consistent with that. I have had a period where I did just set an alarm and put my phone away and just go right to bed.
And, all though I’ve never had a separate alarm I’m pretty sure it would go well for a while before I have a day where I bring my phone into my room for whatever reason and boop mess it all up.
(x & y) ∨ (x & !y)
11 = 1 & 1 ∨ 0 & 1 = 1 ∨ 0 = 1
10 = 1 & 0 ∨ 1 & 1 = 0 ∨ 1 = 1
01 = 0 & 1 ∨ 0 & 1 = 0 ∨ 0 = 0
00 = 0 & 0 ∨ 0 & 1 = 0 ∨ 0 = 0
What’s the symbol for “or” in relation to ! being not, & being and.
~4 minutes