0:13 lecture that is a set of operations
1:53 and you can find
1:56 the sets that nomination
1:58 we have a different kind set of preparations
2:05 given a sets of a and b the sets
2:09 theoretic operators are
2:10 union of u
2:13 and we have intersection of u
2:16 differences or difference difference
2:20 or
2:23 complement was symmetric
2:24 symmetric differences
2:26 differences
2:32 and minus and then we have the
2:51 first we have
2:54 young chinese having union okay pakistan
2:57 for example a union of b and
2:58 and or
2:59 or
3:02 a intersection of b
3:05 or a difference
3:06 of me
3:09 and then complement of a
3:12 and then cement the difference of b
3:21 the union of the sets a and b is the set
3:23 that contains those elements that are
3:51 is equal to sets
3:54 of x such that x is an element of a or
4:18 polynomial intersection
4:20 so intersection of the sets a and b is
4:22 the set that containing those elements
4:24 in both a
4:25 and b
4:43 a is
4:44 intersection of b
4:48 equals to the set of x such that x is an
4:57 okay so example i think i remember you
5:01 know what you see on me money uh
5:02 accountability manager
5:05 at scholar so exciting
5:07 so in the example latin
5:24 actually this
5:42 so if a and we have no common elements
5:43 they are
5:53 so therefore there are no common
6:05 okay try nothing to perform these
6:08 indicate operations okay so number one
6:10 so we have sets
6:12 two three four
6:16 union of three five and seven so
6:39 we have four
6:41 four and
6:42 and next
6:47 five
6:49 next we have seven
6:50 seven
6:51 and so on
8:54 so set of n
8:57 union of set of z or
8:59 integer uh natural numbers and then
9:03 integer okay so alumni then that
9:05 natural numbers are and then
9:07 set of integers so natural numbers one
9:09 two three four and so on
9:11 so i use ellipses
9:12 ellipses [Music]
9:14 [Music]
9:16 next we have here set of integers we
9:18 have negative three negative two
9:19 negative one
9:40 n is
9:43 natural numbers is a
9:45 subset of integers
10:28 all right next number five
10:33 we have natural numbers and intersection
10:34 of a set
10:35 set so
10:36 so
10:38 remember a natural number that is a
10:39 counting number one two three four five majita
10:44 problem intersection
11:11 [Music]
11:13 the difference of a and b denoted by a
11:15 minus b
11:16 is the set containing those elements
11:20 that are in a but not in b okay
11:31 okay
11:33 so we have here
11:39 is equals to set of x such that x is an
11:40 element of a
11:43 and x is not an element of b
11:44 b okay
12:09 the complement of set a is the
12:13 complement of a with respect to set of u
12:15 or therefore the complement of set of a
12:18 is u minus a or a set of a u minus set
12:20 of a
12:48 so complement of a
12:50 is equal to
12:54 set of x such that x is an element of u
12:55 set u
12:57 and x is that
13:05 for example check
13:07 so we're looking for that okay so this
13:10 is left a one two three four five
13:13 elixir b7 three one two three four five
13:14 six seven eight nine ten
13:16 and then b is three five seven and nine
14:15 okay
14:18 so b minus a so check that in b
14:46 let you is equal to set u is equal to
14:50 set of m x and a l t p h and
14:58 set of x and l p okay check that x
15:13 find y so
15:14 so
15:18 complement of y is equal to u minus y
15:20 y so
15:26 that is m a
15:28 a d
15:29 d h
15:35 [Music]
15:37 number four [Music]
15:40 [Music]
15:42 so let a
15:45 be the set of all of positive integers
15:48 greater than 10 with universal set of
15:49 the set
15:51 of all positive integers so find
15:53 complement of a
15:56 so checking attendee that
15:57 that
15:59 scripture 10 is 11
16:01 12 13
16:10 while for the universal set or
16:12 in the end
16:13 they are all positive
16:15 in the years
16:17 okay so i don't know how we positive
16:20 integers so we have positive one opacity
16:24 two positive 3 4 and so on
16:28 so we're looking for a complement of a
16:31 complement of a is e set of view minus
16:33 set of a
17:19 elements in exactly one of the two sets and
17:21 and because
17:23 because
17:27 nothing intersection union offsets a and
17:34 symmetric difference asymmetric
17:37 difference of b and sometimes the symbol
17:39 represents by triangle for example yandy
17:41 ba you know a
17:42 a
17:44 symmetric of b
17:45 is equal to
17:48 set of such a set of x such that x is an
17:50 element of a
17:52 and symmetric difference of x
17:55 and then an element of b
17:56 where sometimes
17:58 it won't you need again a symbol triangle
18:33 and
18:35 okay for example let a is equal to one
18:38 two three four five seven and nine and
18:40 then two four six eight and ten
18:43 and then c is one two three four five
18:45 okay so a
18:46 a
18:48 symmetric difference of b and
18:49 and
18:53 b symmetric difference of c
19:13 so one two
19:14 two
19:16 one three five
19:17 five six
19:18 six seven
19:19 seven
19:22 eight nine and ten excuse
20:01 so let a and b
20:03 b sets then a
20:04 a symmetric
20:36 symmetric difference of a
20:39 symmetric of difference of b is equal to
20:42 b symmetric difference of a
20:44 and tau genetic community
20:47 so a symmetric difference of b is just
