a) $\neg m \implies \neg f \lor \neg e$
b) $(a \land n) \implies (a \lor \neg n)$
Ano, b je tautologie.
| p | q | r | p ∧ ¬ r | r ∧ ¬ q | (p ∧ ¬ r) ⇒ (r ∧ ¬ q) | |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 1 | |
| 0 | 0 | 1 | 0 | 1 | 1 | |
| 0 | 1 | 0 | 0 | 0 | 1 | |
| 0 | 1 | 1 | 0 | 0 | 1 | |
| 1 | 0 | 0 | 1 | 0 | 0 | |
| 1 | 0 | 1 | 0 | 1 | 1 | |
| 1 | 1 | 0 | 1 | 0 | 0 | |
| 1 | 1 | 1 | 0 | 0 | 1 |
a) Ne.
b) Ano.
c) Ne.
d) Ne.
e) Ne. viz. a)
| p | q | r | (r implies p) ∨ ¬(q ∧ r) |
|---|---|---|---|
| T | T | T | T |
| T | T | F | T |
| T | F | T | T |
| T | F | F | T |
| F | T | T | F |
| F | T | F | T |
| F | F | T | T |
| F | F | F | T |
a) Ne.
b) Ano.
c) Ano.
d) Ne.
e) 1., 2.
f) Není
| p | q | r | (p ∧ ¬ r) ⇒ (r ∧ ¬ q) | (r implies p) ∨ ¬(q ∧ r) | |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | |
| 0 | 0 | 1 | 1 | 1 | |
| 0 | 1 | 0 | 1 | 1 | |
| 0 | 1 | 1 | 1 | 0 | |
| 1 | 0 | 0 | 0 | 1 | |
| 1 | 0 | 1 | 1 | 1 | |
| 1 | 1 | 0 | 0 | 1 | |
| 1 | 1 | 1 | 1 | 1 |
a) $(p \land \neg q) \lor r$
b) $(p \land \neg q) \lor (\neg p \land q) \lor r \lor s$
a)
b) $((\neg p \lor q) \land (\neg p \lor r)) \lor ((p \land \neg q) \land (p \land \neg r))$
a) Nelze.
b) $r = q = \neg p = 1$
a) Ano.
b) Ne.