Гладкий А.В. Введение в современную логику
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A
A ≡ A
A A ≡ A A
≡
≡
≡
≡
≡
≡
2+2 = 4 ≡
2+2 = 5 ≡
ABC
A, B, C
∈
a ∈ A a A
a A A a
a A a A A a
a ∈ A
a A A
a a A
/∈
M 2 ∈ M
−5 /∈ M 0 ∈ M
A
B A
B A B
B A
A ⊆ B B ⊇ A
A
B
C
D
B ⊆ A C ⊆ A D ⊆ C D ⊆ A
A ⊆ A B ⊆ B C ⊆ C D ⊆ D
A A A
A B
A B A B
A B B
A A ⊆ B B ⊆ A
A B A = B A
B A = B
A B C A = A A = B
B = A A = B B = C A = C
A ⊆ B A = B A
B
B A ⊂ B B ⊃ A
B C D
A D C
−3
{2, 7, −2, 1/2}
−2 {7, −2, 2, 1/2}
{1/2, −2, 2, 7}
{1, 2, 3,...,100}
{0, 2, 4, 6,...} {1, 4, 9, 16,...}
{x | x }
{2n | n =0, ±1, ±2,...}
{x | x x<−5}
−5
{1, 2, 3,...,100} = {x | x 0 <x<101}
{x
2
| x }
{x | x }
{1/2, 1/3, 1/4,...,1/1000}
{1, 8, 27, 64, 125,...}
{x | x 1 <x<4} = {2, 3}
{x | x 1 <x<3} =
= {2}
{x | x 1 <x<2}
∅
{x | x 1 <x<2}
A ∅ ⊆ A