logika zadania


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( Ł )
( )
[( )Ł ] ( Ł )
( ) [( ) ( Ł )]
( ) ( Ł )
( Ł ) ( )
( Ł ) ( )
[( ) ] [ ( )]
((( ) ) )
2


( )
Ł ( )
> 0 > 0 > 0.
2
2
= 0
2
-
3
-
3
+
4 2
-
+
> 1 > 1 > 1
2
< 0 < 0 < 0
3
2
3
log2 3
log3 5
,
ł
p 0 Ł ł 0 + Ł max ,
{ }
+ Ł +
- ł -
- Ł +
+ ł -
=
=
(( ) )
( ) ( Ł )
(( )) ( Ł )
Ł
Ł Ł Ł Ł
4
= {0,1,2,3,....,17}, = {2,4,6,8,10}, = {1,3,5,17}, = {1,5,6,8,17}, = {6,12,13}


-
( )
-

= {2,4,5} = { : }
= { : < 0}
, , ,
, , - , -
= { : . 3}
2
= { : = 1}
= { : 2 Ł 2}
1
= - 0 : + ł 2ż
{ }


Ć
[1,5)[- 2,3]
[-1,3] (2,Ą)
[0,5]-[2,7)
[0,5][2,7)
5
[0,Ą]
[0,4] Ć
, , \
2

3 4 +16
= : - = 0ż, = { : -1 + - 5 > 8}

2
-1 +1


1
= :3 log + 2log = 2ż, = { : log2( -1)- 2log( -1) > 0}


= { : +1 + 2 = 2}, = { : +1 - -1 = 1}
1-

1
ć
= { : - 3 + + 4 = 9}, = : Ł 1ż


2
Ł ł


1 1+
,
= : < = : > 1
ż ż
1-

2

+1 2
= : > {
ż, = : + 2 > 3}
+1

2
2

( + 3) ( + +1)
= : > 0 = { : -1 Ł 5}
ż,
(4 - )

= { :log -2( -1) > 1}, = { : 2 -1 < + 3}
= { , }, = { , , , , , }, = { * : .( ) ł 2} = { * : ( ) Ł 2}
, \ , \ ,
, , , \
* - , * -

2
\ = \ ( )
= ( ) ( \ )
\ ( \ ) =
- - = -
( ) ( ) ( )
6
\ ( \ ) = ( \ ) ( )
( \ )\ = \ ( )
( ) = ( )





Ć
=
( ) = ( )
( \ ) =
( )\ =
( )
=
=
= =

=
=
ą \ ą \

7
1
-1,
[0,1] =

ę
2
ł
= {1,3,5}, = {2,4} = {1,5} ( ) =
= { , , } = { , , }


{( , ) : = }
= {0,1,2,3} = {1,3}

{( , ) : Ł }
{( , ) : ł }
{( , ) : + ł 3}
{( , ) : > 5}
{( , ) : = }
,
= [0,1], = [2,3]
= [- 2,1], = [0,3]
= [0,1], = {- 2}
= (- Ą,1), = (2,Ą)
2
{( , ) : > }
2
{( , ) : + = 2}
2
{( , ) : Ł 4}
2 2
{( , ) : > }
2
{( , ) :max{ , }> 5}
2
{( , ) :max{ , }Ł 1}
,
8
2 2
= {( , ) : sin( - ) = 0}, = {( , ) : = 0}
2 2
= {( , ) : sin( + ) = 0}, = {( , ) : cos( - ) = 0}
2 2
= {( , ) : ( + ) = 0}, = {( , ) : cos( + ) = 0}
2 2
= {( , ) : ( + ) = 0}, = {( , ) : = 0}

2 2
= {( , ) : log = log }, = ( , ) : = 1ż


,
= { : Ł 2}, = { : -1 < 2}
= { : + 2 ł 1}, = { : - 2 < 1}
2

- 2 +1
= : ł 0ż, = { : 0 < < 3}

4 - 2


16 - 2
= { :1 < < 5}, = :
3 ł 0ż
+ 27

2 -1
2
= { : log2 ( -1)< 3}, = : < 1ż

+1

2

- 2 + 3 - 5

2
= : ł 0 = { : log0,5 ( + 5 + 6)< -1}
ż,
3 - -1


( ) = ( ) ( )
( ) = ( ) ( )
9
" = 2

2
+ 2
" ł

+1 +1
1 1
$ ł

+ 1 + 2
3 +1
" ł 0

2 +1
2
- 2 + - 4
$ Ł 0
2

- 3 - 2
2
2 - 4 + 2
$ Ł 0
2

- 2 - 3
" ( = 3 = 3 )
,
" ( + ą 3 + = 3), = {1,2,3}
,
2 2
$ $ + = 10

" $ Ł

-
2
" $ = - 4

+
,
"$[2 = ]
$"[2 = ]
"$[2 = ]
$"[2 = ]
""[{2 = }]
,
"$[ = 0]
$"[ = 0]
"$[ = 1]
10
$"[ = 1]
$ ( ) " ( )
"$ ( , ) $" ( , )
" ( ) " ( )
"ć$( < ) ( + Ł )

Ł ł
"(("f( )y ( ))y ( ))
"( = ) = 0
"
Ł " ( ( ) Ł ( ))

+ = 3 3 + 3 = 5
f( ),y ( ),
" (f( )y ( )) " f( ) " y ( )

$ f( )Ł $ y ( ) $ (f( )Ły ( ))

11
ł
= , 2
-2
1 1
ć
= - ,

Ł ł

-1
( )
= , 2
ę

ę
ł
= 1, 2,...,3
{ }
= [ , +1]
= { : = sin },
= { : Ł 1}, -{0}
= { : +1 Ł },
+
= { : < },
+
= - ,
[ ]
1 1
ć
= - ,

Ł ł

-1
( )
= , 2
ę

ę
ł
= 1, 2,...,3
{ }
= 2 1, 2 3, 2 5, 2 7,..., 2 ,... ,
{ }
\ = Ć
- - )
U U U(

- ) -
I( I I

12
)
U( U U

13
= {1,2,3,4} = {5,6,7,8}
( , ) + Ł 10
( , ) + = 10
( , ) +
, , , = {0,1,2,3,4}
1 2 3 4
( , ) +
1
( , ) Ł
2
( , ) - = 0
3
( , ) -
4
= {a, b , c,e}
\ a b c e
a + + - +
b + + + -
c - + + +
e + - + +
( , ) -
1
( , ) - . 3
2
( , ) - Ł 5
3
( , ) min{ , }= 2
4
( , )
5
14
( , ) + 2
6


= {4 + : = 1,2,3,....}, = 0,1,2,3
= { , , , } = 2
( , ) =
= { , }
= 2

( , ) =
( , )
0 0 0 0
( , ) ( , ) = =
15
( , , )
( , , ) ( , , ) =
1 2 3 1 2 3
mod
( , ) mod = (mod )
= (mod ) $ = +

= (mod ) = (mod )
+ = ( + )(mod )
- = ( - )(mod )
= ( )(mod )
16
:
3

, ł 1

( ) = , 0 < < 1

- , Ł 0
2

, - , -1
[0,1]
17
= {1,2,3,4,5}
( ) = 6 -
( ) = max{ ,3}
( ) = min{ ,2}
( ) = min{5, }
2
( ) =
+1
1
( ) =
2
- 4
( ) = log(sin )
( ) = ln( - )
1+
( ) = + 3
1-
2
( ) = arcsin
1+
2 2
( ) = + 2 ( ) = 2 +
2
( ) = ( ) =
2
( ) = ( ) =
( ) = ( ) = 1
( ) = 1 ( ) = sin2 + cos2
( ) = 1 ( ) =
3
( ) =
2
( ) = -
1
( ) = sin
18
1
( ) = +
( ) = sin + cos
2
( ) =
2 - 4
( ) = log(sin )
2
3 4
( ) = - 3 ( ) = ( ) = ( ) = 2
2
+ 2
o o
o o
o
o
o
2
( ) = , (- Ą,0]
3
( ) = ,
5
( ) = -1,
1
( ) = , > 1
-1
( ) = , ł 0
1
( ) = , \ {0}
:
( , )= (- ,- )
( , ) = (2 ,3 )
( , ) = ( + ,- )
( , ) = ( ,-4)
19
( ) = 2 + 3
3
( ) = - 2
3
( ) = ( - 2)
3
( ) = + 3
: :

2 .

( ) = 2 ( ) =

-1 .

2
o = I o ą I
2
( ) =
= [- 2,3], = (1,4)
= (0,2), = {9}
= {- 3}, = (- Ą,3]
1
( ) =
1
ć
= [1,3], = ,4

2
Ł ł
= (0,2), = {9}
( ) = cos 2
= { : ł 0}
3
= : + P Ł Ł P + P
ż
U P
4 4

= { : 0 Ł Ł 1}
( ) = + 2
= [0,1]
= [0,2]
= (- 2,0]
20
= [2,6]
2
( ) = - 2
= [0, 2]
= [0,2]
= [0,2]
= (- 2,0]
= [2,6]
-1
( ) = + 2 = [2,3] ( ( ))
21
[0,2] [0,1]
[ , ] [ , ]
[0,1] [0,1)
[0,1] (0,1)
: , ( , ) = (2 -1)2 -1

= 2,
+ ,
22

( , ) / .
( , )
Ł
Ł " ( ) Ł ( )

Ł .
0,1]
[0,1][
0,1]
Ł [0,1][
Ł " ( ) Ł ( )

Ł .
0,1]
([0,1][ ,Ł)
= \ {1}; /
1
1
= {1,2,3}, = {0,1}
( ) ( ) = ( )
= {1,2,...,7} 2 / -
23


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