Answer:
Sure, I can help you create truth tables for these logical formulas.
Here are the truth tables for each of the formulas:
(a) ¬(P ∧ (Q ∨ ¬P))
| P | Q | ¬P | Q ∨ ¬P | P ∧ (Q ∨ ¬P) | ¬(P ∧ (Q ∨ ¬P)) |
|---|---|----|-------|--------------|-------------------|
| 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 | 0 |
(b) P ⇸ ¬(∧)
| P | (∧) | ¬(∧) |
|---|-----|-------|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
(c) (∧) ⇸ (¬ ⇸ ¬)
| (∧) | (¬ ⇸ ¬) | (∧) ⇸ (¬ ⇸ ¬) |
|-----|---------|----------------|
| 0 | 1 | 1 |
| 1 | 0 | 0 |
In these truth tables:
- P and Q are variables that can take on the values 0 (False) or 1 (True).
- ¬P represents the negation of P.
- Q ∨ ¬P represents the logical OR operation between Q and ¬P.
- P ∧ (Q ∨ ¬P) represents the logical AND operation between P and Q ∨ ¬P.
- ¬(P ∧ (Q ∨ ¬P)) represents the negation of P ∧ (Q ∨ ¬P).
In the second formula, (∧) represents an unspecified logical operation (it's not clear what operation you intended).
In the third formula, (∧) represents an unspecified logical operation, and (¬ ⇸ ¬) represents the logical biconditional (if and only if) operation between ¬ and ¬.
Explanation: