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Mathematical Language and Symbols : Venn Diagram and Sets | Darwin Ong | YouTubeToText
YouTube Transcript: Mathematical Language and Symbols : Venn Diagram and Sets
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Video Summary
Summary
Core Theme
This content introduces Venn diagrams as a visual tool for representing logical relationships between sets, explaining fundamental set theory concepts like universal sets, subsets, proper subsets, and power sets.
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so let's continue our lesson i hope not
lecture regards introduction
so continuation
now we go to the band diagram and sets
okay so
venn diagram is a widely used diagram
style that shows the logical relation
between sets
popular rice nijan ben no 1880s as john ben
ben
so he is an english mathematician
logician and philosopher you know that
for introducing the band diagram which
are used in logic set
jury probability statistics and computer science
set contains all the elements of relevant
relevant
to a given discussion okay so for
example and you know i think
universal set for example marantayon 52
so
sets are represented by circle for
example metallization we have abc so we
can type example
but sometimes
five six seven or what actually one seven
seven
so one two three four so example
it's a band diagram okay
okay
subsets in every set element of set a is
also contained in set b then
then
set a is a subset of
set b in symbol a at you know a is
subset of b
for example we have given one two three
four five six seven nine ten then the
possible subsets are
southern marathon a three five seven
b four eight nine so
and then here yeah
a is a proper subset
of b
a proper subset of b if a is subset b
is equal to sets of one two three and b
sets of one two three four determine if
one two three four
one onion one
and two and
okay if let a is equal to
set of x
such that x is a proper sub positive integer
integer
less than or equal to a b
b
is equal to sets of x
such that x is a positive even integers
less than 10
and then c is
equals to sets of 2 4 6 n
8 and ten
ten
so troll falsa generating number one two
checking attention a is a proper
easy subset of a
and then c is a subset of a and then b is
is
proper sub set of c
subset of universal set
and then c
is a subset of b
troll false huh
huh
and then you number three
so a is a subset of a oh yes
and then no element is
subset of a
for example
if duo is a set
so yeah
no set subset
duo and duo
is a
foreign
no sets or no sub no center or empty sets
so we have eight possible subsets
subsets diva
so apparently power set is the set of
all subsets of another
set the power set of s is denoted by p s
s
and for example write all the power set
yeah and
okay
so that is a
for example
we have one two three four and so
we have four
so n is equal to four so
set one two three four
one two one three one four two three
three two four three four one two three
one three four two three four one two four
four
like one two three four five six seven eight
eight
ten twelve
eight nine ten eleven twelve thirteen
one two three four five six seven eight nine
nine
question
was s the power set of the empty set
so your power of set nut and empty set
is equal to
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