0:08 so let's continue our lesson i hope not
0:10 lecture regards introduction
0:12 so continuation
0:15 now we go to the band diagram and sets
0:16 okay so
0:19 venn diagram is a widely used diagram
0:22 style that shows the logical relation
0:24 between sets
0:28 popular rice nijan ben no 1880s as john ben
0:29 ben
0:31 so he is an english mathematician
0:33 logician and philosopher you know that
0:36 for introducing the band diagram which
0:38 are used in logic set
0:41 jury probability statistics and computer science
0:47 set contains all the elements of relevant
0:49 relevant
0:52 to a given discussion okay so for
0:55 example and you know i think
1:16 universal set for example marantayon 52
1:41 so
1:42 sets are represented by circle for
1:46 example metallization we have abc so we
1:49 can type example
1:51 but sometimes
2:09 five six seven or what actually one seven
2:10 seven
2:13 so one two three four so example
2:15 it's a band diagram okay
2:17 okay
2:20 subsets in every set element of set a is
2:23 also contained in set b then
2:24 then
2:27 set a is a subset of
2:30 set b in symbol a at you know a is
2:31 subset of b
3:05 for example we have given one two three
3:08 four five six seven nine ten then the
3:10 possible subsets are
3:13 southern marathon a three five seven
3:16 b four eight nine so
3:42 and then here yeah
3:54 a is a proper subset
3:56 of b
4:01 a proper subset of b if a is subset b
4:12 is equal to sets of one two three and b
4:15 sets of one two three four determine if
4:23 one two three four
4:25 one onion one
4:26 and two and
4:44 okay if let a is equal to
4:46 set of x
4:49 such that x is a proper sub positive integer
4:50 integer
4:53 less than or equal to a b
4:54 b
4:57 is equal to sets of x
5:00 such that x is a positive even integers
5:02 less than 10
5:04 and then c is
5:07 equals to sets of 2 4 6 n
5:09 8 and ten
5:10 ten
5:14 so troll falsa generating number one two
5:21 checking attention a is a proper
5:23 easy subset of a
5:26 and then c is a subset of a and then b is
5:27 is
5:29 proper sub set of c
7:45 subset of universal set
7:47 and then c
7:49 is a subset of b
8:22 troll false huh
8:23 huh
8:33 and then you number three
8:56 so a is a subset of a oh yes
8:59 and then no element is
9:01 subset of a
9:02 for example
9:05 if duo is a set
9:06 so yeah
9:11 no set subset
9:16 duo and duo
9:17 is a
9:50 foreign
10:01 no sets or no sub no center or empty sets
10:15 so we have eight possible subsets
10:17 subsets diva
10:24 so apparently power set is the set of
10:26 all subsets of another
10:32 set the power set of s is denoted by p s
10:34 s
10:37 and for example write all the power set
11:01 yeah and
11:05 okay
11:07 so that is a
11:43 for example
11:45 we have one two three four and so
11:49 we have four
11:54 so n is equal to four so
12:12 set one two three four
12:16 one two one three one four two three
12:18 three two four three four one two three
12:21 one three four two three four one two four
12:23 four
12:31 like one two three four five six seven eight
12:32 eight
12:34 ten twelve
12:36 eight nine ten eleven twelve thirteen
12:48 one two three four five six seven eight nine
12:49 nine
13:26 question
13:30 was s the power set of the empty set
13:50 so your power of set nut and empty set
13:52 is equal to
