it's a good question. I don't know if I have a good answer. Truth tables are used in what's called Boolean logic, where those are the only possibilities. Could you create something similar that allowed True, False and a 3rd answer like N/A? I suppose so, but maybe it wouldn't be as applicable as truth tables are. Sorry I don't have a better answer for you.
Pal, in like four minutes you got me to understand a concept my Reasoning and Heuristics professor couldn't explain to me properly in a half hour lecture. 10/10 work dude
I'm glad we both wonder about the same thing! But, explain this to me, purely in mathematics, as a counterexample to yours: "If X is a triangle, of which the sum of each angle is 300 degrees, then X is a circle." Why is this statement true?
Yeah, I hear ya. I guess if I were forced to defend the validity of this statement, (I'm not saying that it "should" be true, just that per our rules it is true) I would say something like, "there's no harm in making it true". Because the sum of the interior angles in a triangle is never 300 degrees, there's no harm in calling that statement true. Maybe it would be more clear if the options were "false" and "not false" instead of "false" and "true" and we could say your statement is "not false". I dunno. I guess from a purely logical point of view, your statement is true. Don't believe me? Prove me wrong. Show me a triangle where the sum of the interior angles is 300 and that triangle is not a circle. I'll wait. lol.
@@LearnYouSomeMath well imo, I agree to your intuition at the start of the video, "ambiguous". It isnt true or false. If I claim that this statement is false, other than simply applying the truth table, you cant show me an example where both p and q are True, hence proving this if then statement to be true, right?
@@LearnYouSomeMath btw, love your explanation! before this video, I wasn't able to ask you the mathematical question I asked. I once started a thread on reddit r/math, but the post got removed for random reasons, wasn't able to think of this example
Thank for this series. I just started a discrete math class and was already struggling in chapter 1. The way you explain things really cleared things up.
The way you explained the if x=5 then x^2=25 really made me understand "if then" logic table columns a lot more. Saying if x does end up equaling 3 that doesn't invalidate the statement makes a lot of sense. I don't necessarily think your first example would work very well though because if you did win the lottery it wouldn't necessarily mean you could fly. It'd be like saying if x=3 then y=6. Sure that could be true in certain situations but it definitely isn't true all the time. Just thought I'd provide some criticism (not that it's needed really because the video did help in the end :D)
thats true(not pun intended ahah) the way i see vacuous statements, is that sometimes a vacuous truth might have some meaning /logic behind it(eg the x^25 example) and other times it won't have any real world applicable meaning behind it (eg the not winning the lottery example). so because there can be cases where a vacuous truth has meaning and other case when it does not having meaning, it's easier to just bunch all of them under one category - that they are vacuous truth's because each case *can* be described as a 'vacuous truth' because logically speaking the statement is true , but sometimes it might not make sense and other times it does might make sense. Another example is if i said 'every ball in my bag is red' but in actually my bag is empty, this a vacuous truth, despite my bag being empty, the number of red balls in my bag is equal to the total number of balls in the bag, which is 0, therefore all the balls in the bag are red which makes it a vacuous statement. In this example, this statement has some truth and some disbelief to it so it's easier to bunch it under one category otherwise everything becomes complicated.
Thank u for ur service sir I was struggling with this in my online courses and the way you articulate the logic used in these truth tables videos makes them feel more approachable, exam including these coming up soon and I fully expect to have a solid plan to attack these expressions and form a truth table logically all from your brain, no special calculators or algorithms needed which is a pretty beautiful form of math in the real world.
I have a question ，may I use calculator to find that question？ Because I cannot find out（->）this symbol in my calculator，only find out “and” “or” “xnor” “xor” “neg”……… pls help😢😢😢
2:33 How does that work? "It doesn't invalidate the original statement". What if you don't know if that original statment is true? I guess you can consider it an axiom but your example doesn't make complete sense to me.
