This content appears to be a transcript of a lecture or tutorial explaining fundamental concepts in set theory and functions, including set notation, operations, probability, and different types of functions.
Mind Map
คลิกเพื่อขยาย
คลิกเพื่อสำรวจ Mind Map แบบอินเตอร์แอคทีฟฉบับเต็ม
so let's
function simple examp
so X belongs to n such that X is less
N means natural
numbers natural numbers numberal
8 Simple simple
number R
1 2 3 4 5 6 7 8 9
2 5 into
5 but 5 into 9 5 x so 5 into
9 45 45
37 accepted
xal to
10 5 into 10
10
10
a x such that X belongs to U comma 5x is
greater than
good
sare
Pary all right REM
toal number X is such that a X belongs
okay a set a
two B [Applause]
B belongs to
one
right
2 Cube
8 2 the^ 4 16 2 power 5
question AAL X belongs to n
n 4 is less than
20 x value
one
two one
two 1
okay
Bal p a p of B P of a intersection
B P of a union P of
one p of beta
2 2 5
of P of
bet a b
p a
a intersection
a p of a intersection
P of
a intersection P of
for 2
64 so 64 answer
Rak by uh Char Char
a e
e
er no
so shanto Manan fixed
fixed
16 5 25 36 49 64 81 100 12
[Music] sa
set so a set
set 1
1 4
4 16
2 25 3 six Dot
set onto t
set bage set
b a prime set a prime intersection B Prime just
PB PB man B set sh set Union C set sh set P Union
set P Union b b sorry B
13 so 2 to the power 2 4 2 power
4 2 power form PC
so 0 common one common three
to say and ultimately 1315
c b un
c b un c 1 3 or five
so P of B un
belongs to belongs to P
[Music] PC C
3 13 p b un3
one five done
135 PB Union
PB Union PC belongs to p b Union
PC belongs to p b Union c pro
49 number of G
section value number of intersection H
value number of intersection H intersection B intersection G
number of a plus number of B plus number of C minus number of a union
of C minus number of a union b b Union C
number a intersection b b intersection
okay first of all number of number of B number of C
B three number
three number of Gap
of Gap belly Gap
Bell so number of Gap sorry Gap h
B NG minus
NG minus intersection intersection key h
intersection intersection key h g b
g b [Music]
intersection and then
number of a plus number of B it number of
that and simple okay
number of cricket number of
so a p of a intersection B
4 second first bracket 2 three 2
[Music] oh function
Ys y = root 4- x² [Music]
X such that X belongs to z z Square value less oral to four
value less oral to four Z right
s- 2-1 0 1 2 plus- one plusus
s y = root over 4 -
over 4 - x² 4 minus x
x² 4 minus x square short
X belongs to a or Y belongs to a comma X Val
2 x Val plus one
root3 Val Z
root3 not belongs to root3 root3 not belongs to
S - 2 0
0 02 2
0us 2 0 plus 2
2 domain domain
domain domain set minus 2
0+ dom dom dom do - 2 0 +
belongs to3
- 2 - 1 0 1 2 - 2
2 - 2 -1 0 1 2us
-1 0 1 2us 2us 3- one Inus 2
2us 3- one Inus 2 -1 1
minus one 01 2 domain minus 2 minus one 01 range
function function similar sort of things but main
difference Ty
like so special relation so special Rel
function f Dom
same input sorry
now possible but different output
[Music] possible
= so Yus
function f y 2x F
x + 1 - 1 2x - sorry + 2 -
1 2x - sorry + 2 - 1
1 2x-
2x- 1 x +
1 F half function f of x main
function so 2 into halfus
one 1- 1 is z f of half value zero and f x + 1 value 2x - 1
9 four three 9 or8
three 9 or8 ag8 4 3 9
x minus X say 2 by 2 minus x a function
[Music] pluss
pluss to condition X is not equal to 2
Beal 10 should be
minus [Music]
f f
f f x belongs to
1 2x should be not equal to - 3 x should be not equal to minus
okay function
function function function onto onto
x y - y 2x + 2
y - 2 y + 2
2 x y + 2 y -
x y + 2 y - 2 done
range y belongs to R such that Y is not equal to
Y is not equal to 2 but Y is not equal to
done topic function
inut X1 F of
X1 F of X1 X1 X2
F of X1 F of X2 input this output so X1
different X1 or X2 different different do X1 or X2
