.
1) 3 5 . ?
3 + 5 = 8, ᒺ : ( 3) ( 5). ֳ . , , ' , ᒺ. ᒺ 8; 8 .
2) ᒺ A = { k, l, m, n } B = { n, o, p }.
. ʳ A: n (A) = 4, B: n (B) = 3. A B = { k, l, m, n, o, p } n (A B) = 6. n (A B) ≠ 4 + 3. ? , = { n } , ,
n (A) + n (B) ≠ n (A B).
, 䒺 ᒺ , .
. 䒺 b ᒺ , , n () = , () = b, + b = ( ), = (), b = (), = .
, , , n (A) = a n (B) = b.
:
1) A = { a, b }, B = { c, d } A B = { a, b, c, d } = , , n (A B) = n (A) + n (B) = 2 + 2 = 4, n (A) = 2, n (B) = 2.
2) A = {Δ, Δ}, B = {Ο, Ο} A B = {Δ, Δ, Ο, Ο} = , , n (A B) = n (A) + n (B) = 2 + 2 = 4, n (A) = 2, n (B) = 2.
ij, , . , , .
䒺 , ᒺ ( 㳿). - .
,
: 䒺 .
( ' ).
, 䒺 b, 䒺 , b.
. , n +1 , 1 + 2 +... + + +1 (1 + 2 +... + ) + +1,
1 + 2 +... + + +1 = (1 + 2 +... + ) + +1 .
: .
() : - 䒺 b : + b = b + .
. A, b B, n (A) = , n (B) = b = . 䒺 + b = n (A B). A B = B A ( ᒺ ), n (A B) = n (B A) n (B A) = b + + b = b + - 䒺 .
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() : - 䒺 , b, : (a + b) + = + (b + ).
. A, b B, , n (A) = , n (B) = , n () = , = , B = . 䒺 ( + b) + = n (A B) + n (C) = n ((A B) C). ᒺ (A B) = =A (B C), n ((A B) ) = n (A (B C)) n (A (B C)) = n (A) + n (B C) = + (b + ) ( + b) + + = + (b + ).
: - 䒺 , b, m , = b : .
:
.
1) ( + b) + = ( + ) + b = + (b + );
2) + (b + ) = ( + b) + =:( + ) + b.
: , .
.
( + b) + ( + d) = ( + ) + (b + d) = ( + d) + (b + ).
, , .
ֳ - ᒺ : , ᒺ - , .
䳿 : (1 ), , . 4 .