I ‘ll tell you how to check the subset ... Look at this example - Ex-1 : For example your formula is - C = { 2,3,6} And then if the question comes like - “ Is 2 a subset of this set “ ? Then your answer will be “ 𝘆𝗲𝘀 “, 2 is a subset of this whole set because 2 is an element of this set . If you want to know it briefly, you can say that this set has the number “2” , this is why two is a subset of this set ( Set C ) ... In mathematical formula, you write this way -👇👇👇 2 ⊆ C Meaning ( 2 is a 𝘀𝘂𝗯𝘀𝗲𝘁 of Set C ) * We write “ Set C” because this set is denoted using the letter “ C” ... You can also use another method to write in mathematical way , and that is... 👇👇 2 ⊆ { 2, 3,6 } Meaning- 2 is a subset of set 1,2,3 .. ⊆ - 👈 ( this is the symbol of subset ) And ... If there is any question like ... “ Is 7 are subset of * Set C * ? “ Then you’re answer would be “ 𝗻𝗼“ .. Guess why , ? Because 7 is 𝗻𝗼𝘁 an element of this set .. ( I am talking about the same set that I gave before ) !! And briefly you can say the number 7 is 𝗻𝗼𝘁 in this set ! So in mathematical way , you’ll write ... 7 ⊄ C Meaning : 7 is not a subset of Set C You can also write in this way as : 7 ⊄ { 2,3,6 } Meaning - 7 is 𝗻𝗼𝘁 𝗮 𝘀𝘂𝗯𝘀𝗲𝘁 of set 2,3,6 If you have any other Question , please let me know , don’t worry , i’ll help you ! 😇😇
you said "if the empty set wasn't a subset of the empty set that would mean that the empty set contains an element that the empty set doesn't and obviously that's not true because the empty set has no element." what did you mean by that ?? i don't understand that. Second. i see that an empty set has no element so if we calculate the number of subsets of the power set 2^0 = 1 so the power set has only 1 element but i don't understand why. how do we prove that?
Can you help me solving this one please You roll a four-sided (1, 2, 3 and 4) die 3 times. For this problem we’ll use the sample space with 64 equally likely outcomes. a. Write down this sample space in set notation. b. List all the outcomes in each of the following events. (i) A = ‘Exactly 2 of the 3 rolls are fours’ (ii) B = ‘At least 2 of the 3 rolls are fours’ (iii) C = ’Exactly 1 of the second and third rolls is a 4’ (iv) A∩C c. Find the probability for sets in question b. that is, P(A), P(B), P(C) and P(A ∩ C) d. Are A and B independent events?
Thanks for watching and more calculus lessons are coming! Currently my focus for lessons is the Real Analysis playlist, but I will also be working on other stuff! Also, there is this recent video I did on a particular derivative: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-iS27bcO2Qm8.html
Thanks for watching, Gideon! I'm not sure what you're asking, do you have a particular proof in mind? I have tons of examples of set theory proofs on my channel, just search for whatever you're looking for. Like "subset proofs wrath of math" or "set equality proofs wrath of math" will both bring up all sorts of videos.
Powerset is the set of all subsets of a given set, and for every element there are exactly two possibilities: either it is an element of the subset, or it is not.
Thanks for watching and I am not sure what you're asking. By definition, the power set of A contains all subsets of A, so certainly by definition all elements of a power set are subsets of some other set. Perhaps you're asking if a set can be an element of its own power set. Since every set is a subset of itself, by definition every set is an element of its own power set. Does that answer your question?
@@WrathofMath at 2:46 i understood the 2 because its 2 choices per element but at 1:41 u wrote 2 to the power of its cardinality which is 0, but in 2:45 u wrote 2 to the power of its cardinality which you used |S|, why is that?...sorry for my english!
At 1:41 I could have written 2^|S|, but that's the same as 2^0 since, in that example, |S| = 0. At 2:45, S is a different set, we are in a different example. Then I wrote 2^|S|, just to remind you of the general formula being used, and in this case |S| = 1, so 2^|S| = 2^1. Does that help?
