subtitlecat.com

All language subtitles for 004 Union of Sets_en

Afrikaans

Akan

Albanian

Amharic

Arabic

Armenian

Azerbaijani

Basque

Belarusian

Bemba

Bengali

Bihari

Bosnian

Breton

Bulgarian

Cambodian

Catalan

Cebuano

Cherokee

Chichewa

Chinese (Simplified)

Chinese (Traditional)

Corsican

Croatian

Czech

Danish

Dutch

English

Esperanto

Estonian

Ewe

Faroese

Filipino

Finnish

French

Frisian

Galician

Georgian

German

Greek

Guarani

Gujarati

Haitian Creole

Hausa

Hawaiian

Hebrew

Hindi

Hmong

Hungarian

Icelandic

Igbo

Indonesian

Interlingua

Irish

Italian

Japanese

Javanese

Kannada

Kazakh

Kinyarwanda

Kirundi

Kongo

Korean

Krio (Sierra Leone)

Kurdish

Kurdish (Soranî)

Kyrgyz

Laothian

Latin

Latvian

Lingala

Lithuanian

Lozi

Luganda

Luo

Luxembourgish

Macedonian

Malagasy

Malay

Malayalam

Maltese

Maori

Marathi

Mauritian Creole

Moldavian

Mongolian

Myanmar (Burmese)

Montenegrin

Nepali

Nigerian Pidgin

Northern Sotho

Norwegian

Norwegian (Nynorsk)

Occitan

Oriya

Oromo

Pashto

Persian Download

Polish

Portuguese (Brazil)

Portuguese (Portugal)

Punjabi

Quechua

Romanian

Romansh

Runyakitara

Russian

Samoan

Scots Gaelic

Serbian

Serbo-Croatian

Sesotho

Setswana

Seychellois Creole

Shona

Sindhi

Sinhalese

Slovak

Slovenian

Somali

Spanish

Spanish (Latin American)

Sundanese

Swahili

Swedish

Tajik

Tamil

Tatar

Telugu

Thai

Tigrinya

Tonga

Tshiluba

Tumbuka

Turkish

Turkmen

Twi

Uighur

Ukrainian

Urdu

Uzbek

Vietnamese

Welsh

Wolof

Xhosa

Yiddish

Yoruba

Zulu

Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:03,330 --> 00:00:04,170 Instructor: Hi there. 2 00:00:04,170 --> 00:00:05,850 In this lecture, we are going to explain 3 00:00:05,850 --> 00:00:09,450 what a union of two events is and how we can use it. 4 00:00:09,450 --> 00:00:12,510 Okay, now we know which part of the graph represents 5 00:00:12,510 --> 00:00:15,240 the intersection of A and B 6 00:00:15,240 --> 00:00:17,910 but what if we only require one of them to occur? 7 00:00:17,910 --> 00:00:19,173 Regardless which one. 8 00:00:20,100 --> 00:00:23,733 That is the same as asking either A or B to happen. 9 00:00:24,660 --> 00:00:28,503 In such cases, we need to find the union of A and B. 10 00:00:29,670 --> 00:00:31,770 The union of two sets is a combination 11 00:00:31,770 --> 00:00:35,103 of all outcomes preferred for either A or B. 12 00:00:35,940 --> 00:00:37,710 If you think about different American states 13 00:00:37,710 --> 00:00:40,680 as separate sets then the citizens of each state 14 00:00:40,680 --> 00:00:42,003 would be their elements. 15 00:00:42,960 --> 00:00:45,450 Just like every Texan is an American, 16 00:00:45,450 --> 00:00:48,150 so is every element of an individual set 17 00:00:48,150 --> 00:00:50,880 also an element of the union. 18 00:00:50,880 --> 00:00:55,680 We denote the union of two sets as A union B, 19 00:00:55,680 --> 00:00:58,260 the symbol we use is just the intersection symbol 20 00:00:58,260 --> 00:00:59,463 flipped upside down. 21 00:01:00,300 --> 00:01:02,250 To avoid confusion between the two, 22 00:01:02,250 --> 00:01:06,183 remember the symbol for union resembles a capital letter U. 23 00:01:08,190 --> 00:01:11,580 Okay, let us examine what the unions would be 24 00:01:11,580 --> 00:01:13,950 in the three different cases. 25 00:01:13,950 --> 00:01:16,620 If the sets A and B do not touch at all 26 00:01:16,620 --> 00:01:19,530 then their intersection would be the empty set. 27 00:01:19,530 --> 00:01:22,830 Therefore, their union would simply be their sum. 28 00:01:22,830 --> 00:01:24,720 Intuitively, this makes sense. 29 00:01:24,720 --> 00:01:27,660 No element is in both sets simultaneously 30 00:01:27,660 --> 00:01:30,483 so we do not need to worry about double-counting. 31 00:01:31,440 --> 00:01:33,000 Going back to the card example, 32 00:01:33,000 --> 00:01:36,930 the union of hearts and diamonds would be all red cards. 33 00:01:36,930 --> 00:01:38,790 No card can have multiple suits 34 00:01:38,790 --> 00:01:42,120 so we need not worry about counting a card twice. 35 00:01:42,120 --> 00:01:45,660 Therefore, the number of red cards equal the union of cards 36 00:01:45,660 --> 00:01:47,973 which are either diamonds or hearts. 37 00:01:49,920 --> 00:01:53,010 If the events intersect, the area of the union 38 00:01:53,010 --> 00:01:55,860 is represented by the sum of the two sets 39 00:01:55,860 --> 00:01:58,500 minus their intersection. 40 00:01:58,500 --> 00:02:00,630 That is because if we simply add up the area 41 00:02:00,630 --> 00:02:02,940 of the two sets, we would be double-counting 42 00:02:02,940 --> 00:02:05,583 every element that is part of the intersection. 43 00:02:06,660 --> 00:02:10,229 For instance, five people in the office have blonde hair, 44 00:02:10,229 --> 00:02:14,070 four people have blue eyes, and only Kate has both. 45 00:02:14,070 --> 00:02:17,430 Therefore, there are only three non-blonde people 46 00:02:17,430 --> 00:02:21,990 with blue eyes and four blonde people with non-blue eyes. 47 00:02:21,990 --> 00:02:25,290 Thus, the union of blonde and blue-eyed colleagues 48 00:02:25,290 --> 00:02:26,760 is the sum of people who have 49 00:02:26,760 --> 00:02:29,370 precisely one of the two features 50 00:02:29,370 --> 00:02:31,473 as well as Kate who has both. 51 00:02:32,700 --> 00:02:37,680 Mathematically this result is three plus four plus one 52 00:02:37,680 --> 00:02:40,170 or eight employees, satisfying at least one 53 00:02:40,170 --> 00:02:41,133 of the conditions. 54 00:02:42,360 --> 00:02:45,570 Alternatively, we can compute the union using the formula 55 00:02:45,570 --> 00:02:47,160 we mentioned earlier. 56 00:02:47,160 --> 00:02:51,840 We have five blondes plus four blue-eyed people, minus one 57 00:02:51,840 --> 00:02:54,150 or a total of eight colleagues who possess 58 00:02:54,150 --> 00:02:57,120 at least one of the two distinct features. 59 00:02:57,120 --> 00:03:00,810 In this instance, the minus one represents Kate 60 00:03:00,810 --> 00:03:02,250 who is the intersection 61 00:03:02,250 --> 00:03:05,253 since she is both blonde and blue-eyed. 62 00:03:06,420 --> 00:03:08,850 We can use the notation we learned so far in this course 63 00:03:08,850 --> 00:03:10,680 to express this. 64 00:03:10,680 --> 00:03:14,220 The union of A and B equals the sum of the sets 65 00:03:14,220 --> 00:03:18,003 of A and B minus their intersection. 66 00:03:18,930 --> 00:03:21,510 In fact, the union formula we just showed you 67 00:03:21,510 --> 00:03:22,980 is universally true 68 00:03:22,980 --> 00:03:25,563 regardless of the relationship between A and B. 69 00:03:27,330 --> 00:03:31,290 Okay, so what happens if B is a subset of A? 70 00:03:31,290 --> 00:03:34,140 Well, in that case, the union would simply be 71 00:03:34,140 --> 00:03:35,733 the entire set A. 72 00:03:36,810 --> 00:03:40,140 Imagine event A is being from the U.S. 73 00:03:40,140 --> 00:03:42,813 and event B is being from California. 74 00:03:43,680 --> 00:03:45,090 If you talk about all the people 75 00:03:45,090 --> 00:03:48,570 who are either from California or the United States, 76 00:03:48,570 --> 00:03:51,603 you are simply talking about all the people from the USA. 77 00:03:52,800 --> 00:03:55,230 Remember that the intersection of these two sets 78 00:03:55,230 --> 00:03:57,840 is equal to the entire set B. 79 00:03:57,840 --> 00:04:00,360 So the intersection of A and B 80 00:04:00,360 --> 00:04:02,553 represents all the people from California. 81 00:04:03,660 --> 00:04:06,660 If we plug this into the formula from a few minutes ago 82 00:04:06,660 --> 00:04:09,210 that would give us the following statement. 83 00:04:09,210 --> 00:04:13,500 The union of all people from California or the United States 84 00:04:13,500 --> 00:04:16,260 is the sum of all California natives 85 00:04:16,260 --> 00:04:21,089 and all Americans minus anybody born in the Golden State. 86 00:04:21,089 --> 00:04:23,790 After canceling out all Californians 87 00:04:23,790 --> 00:04:26,100 we get exactly what we expect. 88 00:04:26,100 --> 00:04:28,680 The union of people from either California 89 00:04:28,680 --> 00:04:32,580 or the United States equals the entire population 90 00:04:32,580 --> 00:04:33,753 of the USA. 91 00:04:35,580 --> 00:04:38,640 Now that we know what unions and intersections are, 92 00:04:38,640 --> 00:04:41,463 we can talk about mutually exclusive sets. 93 00:04:42,390 --> 00:04:43,380 In the next lecture 94 00:04:43,380 --> 00:04:46,320 we are going to define the term mutually exclusive 95 00:04:46,320 --> 00:04:49,560 and discuss certain characteristics of such sets. 96 00:04:49,560 --> 00:04:50,583 Thanks for watching. 7636