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Mathematical Language and Symbols : Set Operations | Darwin Ong | YouTubeToText
YouTube Transcript: Mathematical Language and Symbols : Set Operations
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Video Summary
Summary
Core Theme
This content introduces fundamental set theory operations, explaining union, intersection, difference, complement, and symmetric difference with definitions and examples.
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lecture that is a set of operations
and you can find
the sets that nomination
we have a different kind set of preparations
given a sets of a and b the sets
theoretic operators are
union of u
and we have intersection of u
differences or difference difference
or
complement was symmetric
symmetric differences
differences
and minus and then we have the
first we have
young chinese having union okay pakistan
for example a union of b and
and or
or
a intersection of b
or a difference
of me
and then complement of a
and then cement the difference of b
the union of the sets a and b is the set
that contains those elements that are
is equal to sets
of x such that x is an element of a or
polynomial intersection
so intersection of the sets a and b is
the set that containing those elements
in both a
and b
a is
intersection of b
equals to the set of x such that x is an
okay so example i think i remember you
know what you see on me money uh
accountability manager
at scholar so exciting
so in the example latin
actually this
so if a and we have no common elements
they are
so therefore there are no common
okay try nothing to perform these
indicate operations okay so number one
so we have sets
two three four
union of three five and seven so
we have four
four and
and next
five
next we have seven
seven
and so on
so set of n
union of set of z or
integer uh natural numbers and then
integer okay so alumni then that
natural numbers are and then
set of integers so natural numbers one
two three four and so on
so i use ellipses
ellipses [Music]
[Music]
next we have here set of integers we
have negative three negative two
negative one
n is
natural numbers is a
subset of integers
all right next number five
we have natural numbers and intersection
of a set
set so
so
remember a natural number that is a
counting number one two three four five majita
problem intersection
[Music]
the difference of a and b denoted by a
minus b
is the set containing those elements
that are in a but not in b okay
okay
so we have here
is equals to set of x such that x is an
element of a
and x is not an element of b
b okay
the complement of set a is the
complement of a with respect to set of u
or therefore the complement of set of a
is u minus a or a set of a u minus set
of a
so complement of a
is equal to
set of x such that x is an element of u
set u
and x is that
for example check
so we're looking for that okay so this
is left a one two three four five
elixir b7 three one two three four five
six seven eight nine ten
and then b is three five seven and nine
okay
so b minus a so check that in b
let you is equal to set u is equal to
set of m x and a l t p h and
set of x and l p okay check that x
find y so
so
complement of y is equal to u minus y
y so
that is m a
a d
d h
[Music]
number four [Music]
[Music]
so let a
be the set of all of positive integers
greater than 10 with universal set of
the set
of all positive integers so find
complement of a
so checking attendee that
that
scripture 10 is 11
12 13
while for the universal set or
in the end
they are all positive
in the years
okay so i don't know how we positive
integers so we have positive one opacity
two positive 3 4 and so on
so we're looking for a complement of a
complement of a is e set of view minus
set of a
elements in exactly one of the two sets and
and because
because
nothing intersection union offsets a and
symmetric difference asymmetric
difference of b and sometimes the symbol
represents by triangle for example yandy
ba you know a
a
symmetric of b
is equal to
set of such a set of x such that x is an
element of a
and symmetric difference of x
and then an element of b
where sometimes
it won't you need again a symbol triangle
and
okay for example let a is equal to one
two three four five seven and nine and
then two four six eight and ten
and then c is one two three four five
okay so a
a
symmetric difference of b and
and
b symmetric difference of c
so one two
two
one three five
five six
six seven
seven
eight nine and ten excuse
so let a and b
b sets then a
a symmetric
symmetric difference of a
symmetric of difference of b is equal to
b symmetric difference of a
and tau genetic community
so a symmetric difference of b is just
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