Докажите, что:
1) ;
2) A ∧ A = A;
3) A ∨ B = B ∨ A;
4) A ∨ (B ∧ C) = (A ∨ B) ∧ (A ∨ C);
5) ;
6) .
A | ||
---|---|---|
0 | 1 | 0 |
1 | 0 | 1 |
A ∧ A = A
A | A | A ∧ A |
---|---|---|
0 | 0 | 0 |
1 | 1 | 1 |
A ∨ B = B ∨ A
A | B | A ∨ B | B ∨ A |
---|---|---|---|
1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 |
0 | 1 | 1 | 1 |
0 | 0 | 0 | 0 |
A ∨ (B ∧ C) = (A ∨ B) ∧ (A ∨ C)
A | B | C | B ∧ C | A ∨ (B ∧ C) |
---|---|---|---|---|
1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 1 |
1 | 0 | 1 | 0 | 1 |
1 | 0 | 0 | 0 | 1 |
0 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 0 |
A | B | C | A ∨ B | A ∨ C | (A ∨ B) ∧ (A ∨ C) |
---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 0 | 0 |
A | B | A ∨ B | |
---|---|---|---|
1 | 1 | 1 | 0 |
1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 |
0 | 0 | 0 | 1 |
A | B | |||
---|---|---|---|---|
1 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 |
A | B | A ⇒ B |
---|---|---|
1 | 1 | 1 |
1 | 0 | 0 |
0 | 1 | 1 |
0 | 0 | 1 |
A | B | |||
---|---|---|---|---|
1 | 1 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 1 |