0:08 let's continue our lesson
0:11 regarding some mathematical language and symbols
0:13 symbols
0:16 now we have four basic concepts
0:19 first we have sets functions
0:20 functions relations
0:22 relations
0:24 and binary operations
0:30 introduction regarding through sets
0:31 sets
0:34 okay sabjan a collection of distinct
0:39 objects forming a group
0:42 or a collection of well-defined objects
0:44 called elements and
0:46 member or member
0:58 embraces nothing okay
0:59 okay
1:01 so for example we have abc
1:03 but is nothing else elements
1:04 elements
1:07 breeze attention element
1:10 user a or element b or element c so depend
1:39 that object is not belong to the set
1:41 set
1:44 so for example let me the
1:48 set of soldier signs sorry we have
1:52 capricorn leo virgo towers and libra so
1:55 they are all
2:00 relayo
2:04 is an element of b
2:05 while queen
2:18 okay
2:20 for example
2:22 we have here example zero one two three
2:30 one is an element of s
2:32 s
2:57 ways to describe essence first we have
3:00 roaster and tabler method
3:04 the elements in the given set are listed
3:07 or enumerated separated by comma
3:08 inside the pair
3:13 the set
3:16 v of a vowel in the english alphabet can
3:18 be written as
3:20 v is equal to
3:23 braces the a e i o u
3:25 so a team of members yeah
3:28 so a e i o u so
3:31 they are all vowels
3:35 the set e of even counting numbers less
3:36 than ten
3:38 can be expressed by e
3:39 e
3:42 even numbers we have two four six and
3:45 eight so they are independent sum and
3:49 10 because less than 10 okay now which is
3:50 is
3:55 while for this
3:58 star roster and tabular method
4:01 the set of positive even numbers less
4:02 than one hundred
4:06 can be denoted by for example i had
5:36 why
5:38 while for the rule descriptive method we
5:40 have the common characteristics of the
5:42 elements are defined
5:46 this method uses set builders notation
5:49 where x is used to represent
5:53 any elements or any element of the
5:55 given set
6:00 remember
6:03 x is such that
6:06 such that x is an even number
6:20 our o is equal to x such that x is an ad
6:24 positive integers or integer less than 10
6:28 or x
6:29 x
6:31 such that
6:40 on
6:42 bedding three 27
6:49 rational 91 per entry over five
6:50 five and
6:58 well for the interval notation
7:00 so recall the notation for intervals of
7:04 real numbers when a and b are real
7:06 numbers with a is
7:09 less than or equal to b so we write for example
7:10 example
7:12 so here
7:23 is an element of r or rationale
7:25 a real number is poly mean so that is
7:32 less than or equal to x which is less
7:34 than or equal to p
7:38 so
7:40 on the end
8:09 3.4.2 5.8 6.9
8:59 you know because of that okay
9:01 okay
9:03 note that a and b
9:08 is called close interval from a to b and
9:09 and
9:13 this is a called an open or open
9:21 parametric cardinality refers to the
9:24 numbers of elements in a set
9:25 set
9:27 for example
9:29 a n and then any so it is a
9:32 representative cardinality of a set a
10:06 all sets which either has no elements
10:09 or has elements which could all be
10:17 for example we have here let r not be
10:19 natural numbers less than 40. hindi
10:28 39 casaba
10:32 i don't know if
10:37 i in finite set in our infant set
10:41 in finite set so our sets whose elements
10:44 cannot be listed or unlimited
10:57 we have also have a
11:00 the null set of this set with no elements
11:02 elements
11:11 i mean
11:13 so for example set
11:14 set
11:17 of positive integers between one to ten
11:20 to the positive b
11:28 one to ten are divisible by thirteen merunda
11:30 merunda
11:34 voila so that is a national set next
11:35 next
11:39 set of integers between two and three
12:02 for the equality of sets
12:06 so let a and b be sets if both a and b
12:10 have the same elements then a and a is
12:12 equal to b
12:15 for example check not n a
12:17 a
12:19 has an element of one two three four
12:21 so b
