.
.
I. . - (), ( 1).
II. , .. , , . .
1. , . , . , 2.
2. , , . . , . 3.
3. , . ( 4).
: A = {15, 30, 45 60, 75} , 15; B = {18, 36, 54, 72, 90} , 18.
, . {15, 18, 30, 36, 45, 60, 72, 75, 90} . 90 , .
. , , .
.
.
:
= { }.
. .
:
A = {1, 2, 3, 4, 6, 12} 12;
B = {1,3, 6, 9, 18} 18.
, . {1, 3, 6} .
. , , .
.
.
:
= { }.
, .
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, , .
.
:
A\B = { }.
, .
, .
, , .
: n(A).
A = {12, 25, 47, 84}, n(A) = 4, .. 4 .
, , :
, , :
:
, .
. 20 , : , . , 12 , 10 5 . , 4 , 2 , 2 ?
, , , , , .
:
.
:
, 20 , , .
.
- 67 . 47 , 35 23 . , ?
, . , , , , , , , , . , 23 . 47 , 47-23=24 . 35-23=12 . , , , 23+24+12=59 . 67 , 67-59=8 . , 8 ,
.
8 = 67-(23 + 24+12).
24 , 23 47, 12 23 35.
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8 = 67-23-(47-23)-(35-23) = 67-47-35+23.
24 . . , . , , .
: 24 . . , . , , .
1. 7.
, , 3 5, : 35, 53, 33 55. , 35 53 , . , , . .
, a b, , : (a; b). a () , b - () .
(a; b) (c; d) , a = c b = d.
(a; b) , a = b. 33 55 (3; 3) (5; 5).
, . A = {1, 2, 3}; B = {3; 5}. , , . , : {(1; 3), (1; 5), (2; 3), (2; 5), (3; 3), (3; 5)}.
, , , . .
. , , .
×. , :
A×B = {(x; y) | }.
.
,
A = {m; n}, B = {t, f, k}.
. , , , :
A×B = {(m; t), (m; f), (m; k), (n; t), (n; f), (n; k)}.
, , .. .
. , .
, (3; 6; 7) 3; (8; 9; 2; 6; 3; 5; 7) 7.
, n .
. 1, 2,, n n, 1, 2,, n- n.
. A = {2; 3}, B = {3; 4; 5}, C = {6; 7}.
A×B×C.
. ×× 3 , , , .
A×B×C = {(2, 3, 6), (2, 3, 7), (2, 4, 6), (2, 4, 7), (2, 5, 6), (2, 5, 7), (3, 3, 6), (3, 3, 7), (3, 4, 6), (3, 4, 7), (3, 5, 6), (3, 5, 7)}.
a , b , ab , ..
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n(A×B) = n(A) ∙n(B) = ab.
k , ..
n(A1×A2××Ak) = n(A1) ∙ n(A2) ∙ ∙ n(Ak).
, 3 , 4 , 5 , 3 4 5 = 60 .
.
1. 3 4 . , , ?
. , . n(A) = 3, n(B) = 4. , , .. n(A×B). n(A×B) = n(A) ∙ n(B) = 3 ∙ 4 = 12. , 3 4 12 .
2. , 5; 4 7?
. . A = {5; 4; 7}. , .. A×A. n(A×A) = n(A) ∙ n(A) = 3 ∙ 3 = 9. , , 5, 4 7 9.
, , . , 2 , 5, 4 7:
55, 54, 57, 45, 44, 47, 75, 74, 77.