Conditional Statements: if p then q

My thought process for this have always been:
-If I guessed RIGHT then answered RIGHT, it make sense(it is RIGHT)
-If I guessed RIGHT then answered WRONG, it doesn't make sense (it is WRONG)
-If I guessed WRONG then answered RIGHT, it still make sense (It is RIGHT)
-If I guessed WRONG then answered WRONG, it still make sense (It is RIGHT)
Basically if you guessed Right in the first place, there's no reason for you to answer wrong, otherwise it will make the whole statement wrong(doesn't make sense). But if you guessed wrong in the first place, you cannot assume your answer will be right or wrong. So either way, any kind of conclusion will make the statement right (make sense)

If I study Hard -- then I will pass == Satisfied with result :)
If I study Hard -- then I don't pass == not satisfied with result :(
If I don't study hard -- then I pass == F**k Yeah I am satisfied :D
I I don't study hard -- then I don't pass == F**k it, I didn't study so I am satisfied with results :)
I hope this made better sense, these RUclips videos makes it more complicated sometimes :D

Bless my professor literally rushed through this entire topic in two sentences, gotta hate summer classes

'Vacuous truths' - brilliant! Truth tables were easy right up to the p(false) implies q (true) line, and this has really stumped me. Other videos just say 'memorise the outputs' and failed to explain WHY the outputs were the way they are for conditional statements - memorising was easy but this video really helped me understand the underlying logic - thank you!

This was incredibly helpful. My textbook feels so incredibly over-saturated with unnecessary information and it was overwhelming. The simplicity here and your clear explanation saved my grade this week! Thank you so much!

Thank you for helping my college algebra course make more sense. You rule.

I love a teacher who is enthusiastic and teaches at an understandable speed. Such a good combo. It's so common you only get one of the two.

This is mirrored, are you really left handed!!!
Your Voice guides me

Dude this was so helpful- I'm a visual learner and this is just brilliantly done

Using this to study for the LSAT. Thanks for the video, helps a lot!

Explaining it using the ~p V q logical equivalency really helped me to finally grasp implication. Thanks!

I'm currently studying this for university entrance exam here in Mexico, so I came across this chanel. Your explanation is definitely easier than my textbook but I was still confused with some parts of the video so I will have to watch it as many times as needed to get it all. Thanks for the content.

I was so stumped when I read this in my textbook, I'm prepping for my upcoming math class and want to understand the concepts before class starts. This was VERY helpful! Subscribed!

You're videos are going to be my savior in my discrete mathematics class. My professor is extremely confusing when she's trying to explain pretty much everything. The textbook helped, but there were still some things I needed some clarification on and you explained them perfectly. Thank you so much for taking the time to make these videos.

finally i got the explanation that i want, ur smart and the way u explan is very clear ...thanks a lot

7:08 mins worth it :) Thank you so much, Dr. Trefor Bazett

I’m teaching truth tables to my students and this video is great!

I have an Intuitive explanation. My statement is: “Whenever I wear a blue jacket then I wear black shoes”. So, in the first row, this statement is true. But in the third row, it is also true, because I didn't say, that I wear black shoes only when I wear a blue jacket but that when I wear a blue jacket I wear black shoes (my point is that black shoes are not a condition for anything, I can wear black shoes with whatever I want, but when I wear a blue jacket then I must wear black shoes, so “blue jacket” is a condition that implies black shoes, and not another way around. This means that I can wear a white jacket and black shoes but the statement:” Whenever I wear a blue jacket then I wear black shoes” doesn't have anything to do with this, it is still true that always when I wear a blue jacket than I must wear black shoes. So this implication is not true only when I do something contradictory to what I claim, for example, I say that: “Whenever I wear a blue jacket then I wear black shoes” and then instead I take some other shoes, for example, I wear a blue jacket but I take some red Nike ✔️. Similarly is for the 4th row. But 2nd the row is the only one that is in contradiction with my statement or claim.

Thanks. This was very helpful. Some lecturers understand logic so well that they are unable to explain it. You are not one of those.

"if p, then q" example is "if it is a dog (p), then it is blue (q)." This is logically equivalent to "it is either NOT a dog (p) OR it is blue (q)". It kind of makes sense if I think of it like this...

This explanation was amazing! Thanks to you ill pass my midterm!

Thank you, I finally got it looking this and other your videos!
I had to develop a bit more resonating with myself explanation though.
Hope it will help somebody more as well. :)
Say, my (actually yours from another video :)) implication is:
If it is a dog, then it is a mammal.
Then, my implication is considering a dog (being a mammal) only, not a cat or a table.
I agree (It is true) that when it is not a dog (p = false), then it can be anything -- mammal or not mammal (q is true or false).
Thus, my implication is TRUE in both cases when it is not a dog -- then everything is all right with my implication, and I AGREE that (not a dog) can be anything.
But when it is a dog, then my implication is ONLY TRUE when it is a mammal -- because it is what I specifically imply!
Otherwise, my implication is FALSE. I.e. when it is a dog, and it is not a mammal -- then and only then my implication FAILS.
Only then my implication is WRONG.
CONCLUSION: Implication is FALSE ONLY when it is WRONG!
Let's create a new boolean result: WRONG! :))

this vid has been given to me by the online teacher cuz the quarantine

Thank you for explaining the scenarios where the initial statement is false :)

You saved me so much time studying. Everything just clicked.

Dude, you had me by 4:30 explaining how conditionals arrive at whether they are true or not.

you just save my life !
i started to learn computer science last month, and your teaching give me a purpose !

Cool! So in essence, you cannot derive a false conclusion from a true assumption.
I'm so glad I found this channel. The way you break down and explain concepts reminds me of a former Math teacher that first sparked my interest in Algebra.

Hi, Trefor,
at 6:54, if p=true, q=true, so p→q should be true, ~p=false, then ~p v q=true. Therefore, their Truth table is same which means they are logically equivalent.
Could we write p v ~q=true?
So, the statement becomes Either I study hard, or I don't pass.

Thank goodness for this video, I nearly cried trying to do my geometry homework with no knowledge of what a conventional statement was because my geometry teacher didn't explain what those where to anyone in the class.

I'm learning from you not only the information but the skill of delivering the information. Thank you for your efforts.

how he is writing

best explanation I found on you tube, thanks man

So that means IF I don’t study hard THEN I will pass the test anyway?

Really great , I was really confused before watching ur video. Now my concept is crystal clear. Love u dude.

This helped me so much. Thank you, your truly saving many students

Thank you so much for this video Dr. Bazett!! I had been spinning my wheels on this Critical Thinking module for the past six hours when I came across this video. Super helpful!!
You're definitely getting a sub from me!

Thank you So Much Sir 🙌. Your Video Helped me Understand the very thing I was having a doubt in.
This one was Precise and Short 👍

You gave me a complete idea and you opened my logic! THANK YOU FOR THIS VIDEO! I needed this , because they taught us this in university, but i didnt understand!!! but now I do! The way you teach is wonderfulllll! thanks again! Greeetings from Turkmenistan

much better explained than my professor, thanks :)

It's fun to learn when Marc Gasol is the one teaching you

Thank you for teaching Dr. Trefor, however, I have a question. What if, for example it says "if p is false, then q is true"". Wouldn't this create a different result? It no longer make p->q = ~pVq . Then this rule/law would only apply to "if ... is TRUE, then ... is TRUE", wouldn't it? Can you please correct me if I'm wrong?
(note : the truth table for p is still in the order of : T,T,F,F)

Hi Trefor, thanks for this video. Quite a few books that I referred to skip the last two cases completely or gloss over it without going into even a minimal depth. I see you dint skirt the last two cases and in fact your study/pass example put things in better context.
I'm taking Logic as a subject in a course on Philosophy and can see where this trouble originates. It lies in the epistemology of different philosophies. The classical Western/Aristotelian ( multi valued logic addresses this gap ) version of truth is True/False , 0/1. However classical /ancient Indian philosophy has a layered or more nuanced version of truth. 7 versions, actually, ranging from True to False! Some of the indeterminate ones are - somehow ( or sometimes) true, somehow ( or sometimes ) untrue, Both true and false ( think Both sides claiming victory in a war!), Neither true nor false.....etc. This layered approach to truth is reality of life and where all confusions, conflicts, distrust, outrage arise. When life is black & white, this works perfectly, but breaks down when things are grey. In short, the real answer to the 2 cases when P is "F" should be "unknown".

How do you think about if q then p?

this just made my day like i understand this easily so grateful to you for that

I replayed the last 20s until I understood them, about four times that is. Now I understand, thanks man

This Is An Instant RUclips Classic!

I'm just here because my girlfriend was teaching me this early and I want to take interest in the things she enjoy.. great video now let me go make her happy

I’m studying philosophy right now, which is how I came across your video, but this makes so much sense for understanding Stats since I took it last year. My memory is foggy, but this video helps!

Is this marc gasol? Thanks for the help.

This is why i like literature more😭😭😭😭

so after you make this chart how do you read it to make a conclusion from it?

I'm currently going through your playlist and this is really helping me study for my midterm. Thanks!

Thank you so much! When you put the definition there with the type of statement you listed early on, it helped me SO much. One book I'm trying to read for class is not the most organized for this sort of thing.

Hey Dr. Trefor, you are amazing! Thanks for sharing it.

Thank god there's teachers in youtube

Thank you so much, I couldn't interpret that the statement was based if p was True in all scenarios of the conditional statement.

Sir this is so helpful... It really helped me.

This is helpful.. now u r a part of my JEE journey ❤❤

I was panicking about my exam tomorrow but you saved me thank you 😭

Is it right to think that the last two Truths as a placeholder as we cannot determine them to be false?

Very well explained, maintained lecture quality like a Senior Professor.

That was super helpful! Your teaching was clear and easy to understand. Thank You!

This one gets everyone, every time.

thank you very much. I have finals this week

Dude is very helpful and easy to understand as you teaching visually and we can able understand easily thank you so much and hats off to you for teaching brilliantly.

Do you ACTUALLY have a window your writing on, or is this a special effect? And how can I produce the effect if it is?

how to you construct a truth table for proving that a proposition is not a contradiction?

I wasnt able to wrap my head around why the bottom two rows were interpreted as True until I saw this video, thank you

weird question do you have to write backwards on that board?

Column 3 is identical to column 5. Can I not say that statement and the "Not" statement in row 5 will always be the same?

Thank you !! Helped me a lot in my finals 😢

Hello I am from india this question is in my text book your teaching was easily understanding thank you

Took me a few stop and starts, reviewing and writing but when it clicked... amazing thank you!

Fantastic video. Just finish a chapter on implications and found your video.

Incredible 😁 love from India sir❤

Why would "either or" not be XOR in this case?

4:57 Either my conclusion is True, or my initial assumption is False.
If the initial assumption (p) is False, then I don't worry about my conditional, i haven't even started my assumption.
I went over several documents & classes, and it's the first time it's presented that clearly !
The last example was a bit confusing though, because it looks like you're using an exclusive or.

You are doing Gods work.

In the first "p" and "q" columns , why was the false/false at the bottom true?

The written examples are terrific to understanding the concept. But APPLYING it to mathematical concepts is so HARD to translate into "statements". How is this done effectively?

im a programmer and i was getting really frustrated because this should be a walk in the park for me and I wasn't getting it but turns out It's just an issue of it not "translating" to a language i understand. Really helped when you explained it like hypothesis and conclusion because then I was able to figure out what it means and "translate" it

Wow Good class. Thanks very much

Or is always an inclusive or in this case right? I found the last part to be the most confusing.... because you could not study and still pass right... so in that last or statement it could have been both.

how did the background work like that?

the biconditional ones had confused a lot.
I thought of this example which made a lot of sense to me.
If your friend can fly by himself in the sky then you can too.
The truth value of it is true

This was really helpful, but still left me with questions on problems such as “~rv(~p->q)”

this is it. This is the video you've been looking for to explain this. Look no further-what you need is right here.

is nobody gonna talk about how easy he made writing backwards look? mkay mkay.

Ohhh right. In a certain way, we transform the statement from a conditional if p then q to a statement about the two outcomes, either not p (then ?) or successful q.
Because we cannot verify whether p actually implies q in all cases, we just leave the implied not q out. But it's still the same thing.

underrated video

What if there three variables p q r what will be the conditional output?

Very good explanation. I am reading Discrete Maths by Kenneth and was little confused by the explanation there.

The most intellectual and satisfactory explanation of foundation of this confusing topic.
Take away for me is "If you want to understand the foundations of logic, go to a mathematician".
Highly appreciated. Thanks.
Yet, how can I translate this to a metal detection system operation logic "If metal is detected (P), then set out the alarm (Q)"
"If metal then alarm" is TRUE meaning the system is working as designed,
"If metal then no alarm" is FALSE meaning that the system is not operating correctly,
"If not metal then no alarm" is also TRUE and the system is also working properly, but,
"If no metal then alarm" case considered vacuously TRUE confuses me here. It's not true, it's a false alarm, the system is malfunctioning.
In electronic design, this case should be assigned "DON'T CARE" value (stay put / remain in the last state). But in logic "don't care" is not truth value.
What am I missing to comprehend here?

Tysm! It helped me a lott! God bless you!

How do you do ~p or ~q?

very good explanation. This is what i were looking for!

Saved my ass after 3 years 😂

Thanks for the simple video dude.