. 67 47 , 35 - 23 . , ?
, . , , - , . : , ; , ; , . , 23 . 47 , 47 - 23 = 24 . , 35 - 23 =12 . , , , 23 + 24 + 12 = 59. 67, , , 67 59 = 8 .
. , , , ( ), , ( ), , 47 + 35 - 23 = 82 - 23 = 59 , , , 67 - 59 = 8 , , , ( ) , .
. , 1 2, =1U2. 1 |1|, 2 - |2|. , . , |1| + |2| , 1, - 2, 1 2 . 1 2 , , () - 1∩2, |1∩2|. ,
|1| + |2| = |1U2| + |1∩2|,
|| = |1U2| = |1| + |2| - |1∩2|.
, = 1U2U3.
||=|1U2U3|=|1|+|2|+|3|-|1∩2|-|3∩2|-|1∩3|+|1∩2∩|.
. - , , . 20 , 12 , . 24 -, 12, ( ), , - 17, 6 . ?
1 - ,
2 - ,
|
|
3 - , .
1U2U3 .
|1U2U3|. , ,
1∩2 - ,
1∩3 - , ,
3∩2 - ( ), ,
1∩2∩3 - , . :
|1U2U3|=|1|+|2|+|3|-|1∩2|-|3∩2|-1∩3|+|1∩2∩3|=
= 2 + 24 + 17 12 6 12 + 1 = 32.
.
= 1U2U3U.Un.
:
|| = |1| + |2| + |3| ++ |n| - |1∩2| - |3∩2| - |1∩3| -- |n-1∩n|+|1∩2∩3| + |1∩2∩4| +..+ |n-2∩n-1∩n|+.+ +(-1)n|1∩2∩3∩∩n|.
, , , n =3.
-. - , 1,2,... n, , , , , , , ..
- - , : , , .
, -.
. 100 28 , - 30, - 42, - 8, - 10, - 5, 3 . ?
, , - , , , = 1U2U3, 1 - , , 2 - , 3 - , , I - . -
| | =| I |-|1U2U3|=| I | -|1| -|2| - |3| + |1∩2| + |3∩2| + |1∩3| - |1∩2∩3| = 100 - 28 - 30 - 42 + 8 + 10 + 5 3 = 20.
, , -, .
.
, " ".
" 70 100 , 75 - , 80 - , 85 - . , , , ?"
A1 , 2 - , A3 - , A4 - .
, , ( ) : .
|
|
I = AU = AU = AU ,
:
| I | = | 1∩2∩3∩4| + | U U U |
:
| 1∩2∩3∩4| = | I | - | U U U |
| U U U |≤ | | + | |+ | | + | |
| 1∩2∩3∩4| ≥ | I | - | | - | | - | | - | |
| I | = 100,
| | = | I \ A 1,| = | I | - |A1| = 100 - 70 = 30, :
| | = 25, | | = 20, | | = 15,
| 1∩2∩3∩4| ≥ 100 30 25 20 15 = 10