nice , however I can see why the kids would be confused at the very tail end of the video you were explaining why the 2 notations were the same, you verbalised it correctly but the drawings were not the same while you pointed to them and said "these 2 are the same". Hoping they understood !
De Morgan's laws are being used, for sure. I'm guessing these students haven't been shown De Morgan's laws, though, considering they are using a "count" formula for P(E|K) instead of the "probability" formula.
A little aside: the formal logic concepts of "OR" and "AND" led to the concept of having OR and AND gates as the fundamental building blocks of computer processors, in part because the electronics required to implement them are simple. (Actually, NOR and NAND gates are even simpler to implement.)
Technically, it isn't actually true. Consider 3/9. 3 is prime yet we can still simplify. Better still consider 29/203. 203 is a multiple of 29 so we can simplify to 1/7. The concrete version is that the numerator and denominator are *coprime*. That is, their prime factorisations do not share any prime numbers. Example using prime factorisation: Can you simplify 882 / 605? Well, 882 = 2 × 3² × 7² and 605 = 5 × 11² since there are no shared prime numbers, the fraction cannot be simplified.
Yes, prime on the numerator isn't enough, but the implied thing he didn't say was "and the denominator isn't a multiple of 29", which makes them coprime (given prime number A, any number that's not a multiple of A is coprime with A.
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Thanks a lot Eddie Woo, In this video, I get how to teach my students in more clear ways.
nice , however I can see why the kids would be confused at the very tail end of the video you were explaining why the 2 notations were the same, you verbalised it correctly but the drawings were not the same while you pointed to them and said "these 2 are the same". Hoping they understood !
Morgan laws are useful to explain that last question
De Morgan's laws are being used, for sure. I'm guessing these students haven't been shown De Morgan's laws, though, considering they are using a "count" formula for P(E|K) instead of the "probability" formula.
A little aside: the formal logic concepts of "OR" and "AND" led to the concept of having OR and AND gates as the fundamental building blocks of computer processors, in part because the electronics required to implement them are simple. (Actually, NOR and NAND gates are even simpler to implement.)
I’m not even in school anymore but I just can’t help but to watch his uploads anyway lol
Eddie est un super-prof!
👍
I love the last compliment of E union M, writing it like that, I've never thought of it before~ XD Thanks~
the fact that I watched this vid just to figure out vinn diagram uses in semantics is just.. wow
De Morgan's Laws.
Not (A or B) = (Not A) and (Not B)
“We can’t simplify that because 29 is prime” ? That’s not the only condition whether you can simplify the fraction or not, is it?
Technically, it isn't actually true. Consider 3/9. 3 is prime yet we can still simplify. Better still consider 29/203. 203 is a multiple of 29 so we can simplify to 1/7.
The concrete version is that the numerator and denominator are *coprime*. That is, their prime factorisations do not share any prime numbers.
Example using prime factorisation:
Can you simplify 882 / 605?
Well, 882 = 2 × 3² × 7²
and 605 = 5 × 11²
since there are no shared prime numbers, the fraction cannot be simplified.
Ben Crossley You are correct. Hé did not mention coprime, just prime on nominator
Yes, prime on the numerator isn't enough, but the implied thing he didn't say was "and the denominator isn't a multiple of 29", which makes them coprime (given prime number A, any number that's not a multiple of A is coprime with A.
Are you colour blind ?