This document discusses mathematical concepts including sets, operations on sets like union and intersection, and functions. It defines concepts such as: - Sets and their elements - Operations on sets - Functions as mappings between sets - Properties of functions like being one-to-one or onto - Relations between sets defined by functions

1. × ∗ ! " # " ! ∗
$ " ∗ " #
∗
→×
"
% & # ! ' (
)*
• ! + × " " " " ,
• & ÷ # - -
-
• # " #
( ( & . /
• # Ω # Ω " ! ∪ ∩
• # 0 "
1 " "∗ ! #
$ $ & !
% ( ∗ & ( " " " ∗∗=∗∗
& / ! 2! ∗∗
3 & !
% ( ∗ & ( " " " ∗=∗
)!
∈ % ( !! ∗ ( " "
=∗=∗ * ! ! & / &! 0! ( ∗ #
&
# !! ∗ " # ( #
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2. 1!
# *!! " =∗= 44 5 ! !&
0 ( " 0 ( #
1!0
∗ & # !! ∗"
( "∗ 2 ∗ & " ( 2
0
)* "+ 2 0
1 ! (
% ( ∗
# *!!
% ( # ! ( ∗ ( =∗=∗ 44
∗ & " !! ! ( ∗"
# ( #
1!
# ## ! ( "
444444444444 =∗=∗∗=∗∗=∗=
6
!! ( ! ( ! $ "
×" # !! ! ! 7{ }"−
) 0 " " ×" ' 8 & 9
8 & 9 ' ( 8 ! ( 9 8 ! 9
) 1 & !
% ( # *5 ! : % ( ∗
& : ( " " " :: ∗∗=∗
:: ∗∗=∗
"∗ ! ; #
% ( ∗ ( " " " ∗
1 " ( ∗ !0 " "
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3. <
"∗ 2 " ∗ & $ # !!
! ∗
) 00
" *!! % #" # ! ( " #!!
%
=∗=∗∗=∗∗∗=∗∗∗ 444444
) =∗=∗∗=∗∗∗=∗∗∗ 444444
1 ∈∗ " ! ( ∗ ∗ ∗4
" # ∗ % !0 "
∗= 0> &
" " " ∗= # ( 7
∗ $ =
∗
→∗
∗ & " ∗= & "
∗ & " ∗= & "
< ∗" " ∗=
!! ! ( ∗" !!
" " ! ( ∗=
? % # *5 ! : !0 / := "
∗ & :" ∗= @ & :=
1!
∗ & " " !! "
∈ %
=== ∗∗=∗∗=∗∗=∗∗
) === ∗∗=∗∗=∗∗=∗∗
1 ==== ∗∗=∗∗
! ! & ∈
1#A #! ! ∗∗=∗∗ ==== # & ! ∗=
∗ & "" ∈
% " !!
== ∗=∗=∗=∗
1 ∗=∗ ==
# & "" ∈ 1 ∗= &
< ( # ∗" !
$ # → " !! " " ∗= ) 00
"∈ % " !!
= =∗=∗=∗
= =∗=∗=∗
1 =∗=∗ == 1 ∗=
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4. ( !! ! ( ∗
" ! ( ∗ % ∗
$ " "∈ " 4 → ! ( ∗=
) 00 "∈ % " !!
=∗=∗=∗ 44=
=∗=∗=∗ 4=4
1 =∗=∗ =44= A →
1 !! " " ! ( ∗=
? ∗ & : " " !! "
% " !!
=:===:=
:::=:==
∗∗=∗∗=
∗∗=∗=∗=∗
=:===:=
:::==:=
∗∗=∗∗=
∗∗=∗=∗=∗
=:==:== ∗∗=∗ =:===:= ∗∗=∗
! ! & """ ∈ 1 ∗= & :=
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