Логика. Множества. Вероятность. Лексаченко В.А. - 46 стр.

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4)
1. A
∧(A
∨
B) |
= A 4. A
|=
A
∨
B 7
. |=
A
→
A∧
(
A
∨ B
)
2
. |=
A∧(A ∨ B)→
A 5
. A, A ∨ B
|=A
∧(
A ∨
B) 8
.
|
=
A ∼
A
∧(
A ∨ B)
.
3. A
|= A
6. A |= A∧(A
∨ B
)
5)
1.
A
∨
B, A |
=
A ∨
B 4.
A
∨
B, B |
=
A ∨
B 7.
A, B
|
= A
∧
B
2. A ∨
B, A |=
A ∨
B 5.
A ∨
B, B |=
A ∨
B 8.
A ∨
B |=
A∧B
3. A
∨
B |= A
6
. A
∨
B |= B
9
. |= A
∨
B → A
∧
B .
6)
1. A
|
= A
4
. A, A
|
= A
7
. |
=
A ∼ A .
2
. |
=
A
→
A
5
. A |= A
3
. A, A
|
=
A
6
. |=
A → A
7)
1.
A, A
∧
B
|= A 4.
B, A
∧
B
|= B 7.
A
∨
B
|
= A
∧
B
2
. A, A∧B
|=
A 5. B, A∧B
|=
B 8.
|=
A ∨ B → A∧B .
3
.
A
|=
A
∧B
6
.
B
|=
A
∧B
8)
1. A∧
B
|
=
B 5. |
= A∧
B
→ B
∧A
9
. B∧A
|=
A∧B
2
. A
∧
B |=
A 6
. B
∧A
|=
A 10.
|
= B∧A →
A
∧
B
3. B, A |
=
B∧A
7. B∧A
|=
B
11
. |
= A∧
B
∼
B∧
A .
4. A∧
B
|
=
B
∧
A 8. A, B |= A
∧
B
9)
1. A ∨ A, A |
= A ∨
A 4
.
A ∨ A, A |
= A ∨
A 7
. |=
A ∨ A
2
.
A ∨ A, A |
=
A ∨ A 5
.
A ∨ A, A |
=
A ∨ A 8
. |
= A
∨
A .
3
.
A ∨ A |
=
A 6
.
A ∨ A |
=
A
10)
1. A∧
A |= A 4. A, A |=
A∧
A 7.
|= A
∼ A
∧A .
2
.
|
=
A∧
A
→ A
5. A |=
A
∧
A
3
. A |
=
A 6
. |
= A →
A
∧A
19 .
Metodom rezolci$i dokazat~ tavtologii (sm. primer 2.4).
1) |
= (
A
→ B)∧A
→ B ,
2)
|= (A
→ B)∧(
C → D
) → (A∧C → B
∧D
) ,
3) |
= (A
→ B) ∨ (C
→ D) → (
A∧C
→ B ∨ D) ,
4)
|= (A
→
B
)∧
(
C
→ B
)
→ (A ∨
C
→
B) ,
5) |= (
A
∨
C
→
B
) → (A → B
)
∧(
C
→
B
)
,
6) |
= (
A∧B
→ C
) → (A → (
B → C)) ,
7) |
= (
A → (
B →
C)) →
(
A∧B
→ C
) ,
8)
|= (A
∧
B →
C
)
→
(
A
∧
C → B) ,
9) |= (A
∧
C → B)
→ (A∧
B → C
)
,
10)
|
= (A
→ B)
→ (
A
∧
C
→ B∧
C) .
46

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