8.13 Propositional logic tutorial
1.The proposition is true since both propositions are true/false
e.g.: There are two propositions: P, Q in only one proposition.
If p and q are both true/false, then \(p⇔q\) is true
(\(2^{3}=8\), if and only if 49 is a perfect square)
2.Solving Strategy:
Example: Determine whether following statements are logically equivalent. ==Using truth table== \(\neg(P\Rightarrow Q)\), \(P\cap \neg Q\)
| P | Q | \(P\Rightarrow Q\) | \(\neg(P\Rightarrow Q)\) |
|---|---|---|---|
| T | T | T | F |
| T | F | F | T |
| F | T | T | F |
| F | F | T | F |
| P | Q | \(\neg Q\) | \(P\cap \neg Q\) |
|---|---|---|---|
| T | T | F | F |
| T | F | T | T |
| F | T | F | F |
| F | F | T | F |
| Clearly, they are equivalent. |