0.2.3.
Solution.
- \(P \wedge Q\text{.}\)
- \(P \imp \neg Q\text{.}\)
- Jack passed math or Jill passed math (or both).
- If Jack and Jill did not both pass math, then Jill did.
- Nothing else.
- Jack did not pass math either.
\(P\) | \(Q\) | \(P \wedge Q\) | \(P \vee Q\) | \((P \wedge Q) \rightarrow (P \vee Q))\) |
T | T | T | T | T |
T | F | F | T | T |
F | T | F | T | T |
F | F | F | F | T |
\(P\) | \(Q\) | \(\neg Q\) | \(Q \rightarrow P\) | \(\neg Q \vee (Q \rightarrow P))\) |
T | T | F | T | T |
T | F | T | T | T |
F | T | F | F | F |
F | F | T | T | T |
\(P\) | \(Q\) | \(R\) | \(\neg Q\) | \(R \rightarrow \neg Q\) | \(P \vee (R \rightarrow \neg Q)\) |
T | T | T | F | F | T |
T | T | F | F | T | T |
T | F | T | T | T | T |
T | F | F | T | T | T |
F | T | T | F | F | F |
F | T | F | F | T | T |
F | F | T | T | T | T |
F | F | F | T | T | T |
\(P\) | \(Q\) | \(R\) | \(P \rightarrow (Q \vee R)\) | \((P \rightarrow Q) \vee (P\rightarrow R)\) |
T | T | T | T | T |
T | T | F | T | T |
T | F | T | T | T |
T | F | F | F | F |
F | T | T | T | T |
F | T | F | T | T |
F | F | T | T | T |
F | F | F | T | T |
\(P\) | \(Q\) | \(P \rightarrow Q\) | \(\neg Q\) | \(\neg P\) |
T | T | T | F | F |
T | F | F | T | F |
F | T | T | F | T |
F | F | T | T | T |
\(P\) | \(Q\) | \(R\) | \(P \rightarrow (Q \vee R)\) | \(\neg(P \rightarrow Q)\) |
T | T | T | T | F |
T | T | F | T | F |
T | F | T | T | T |
T | F | F | F | T |
F | T | T | T | F |
F | T | F | T | F |
F | F | T | T | F |
F | F | F | T | F |
\(P\) | \(Q\) | \(R\) | \((P \wedge Q) \rightarrow R\) | \(\neg P \vee \neg Q\) | \(\neg R\) |
T | T | T | T | F | F |
T | T | F | F | F | T |
T | F | T | T | T | F |
T | F | F | T | T | T |
F | T | T | T | T | F |
F | T | F | T | T | T |
F | F | T | T | T | F |
F | F | F | T | T | T |
\(P\) | \(Q\) | \(R\) | \(P \rightarrow Q\) | \(P \wedge \neg Q\) |
T | T | T | T | F |
T | T | F | T | F |
T | F | T | F | T |
T | F | F | F | T |
F | T | T | T | F |
F | T | F | T | F |
F | F | T | T | F |
F | F | F | T | F |
\(P\) | \(Q\) | \(R\) | \(\neg P \imp (Q \wedge R)\) |
T | T | T | T |
T | T | F | T |
T | F | T | T |
T | F | F | T |
F | T | T | T |
F | T | F | F |
F | F | T | F |
F | F | F | F |
\(P\) | \(Q\) | \(R\) | \(P \imp Q\) | \(P \imp R\) | \(P \imp (Q \wedge R)\) |
T | T | T | T | T | T |
T | T | F | T | F | F |
T | F | T | F | T | F |
T | F | F | F | F | F |
F | T | T | T | T | T |
F | T | F | T | T | T |
F | F | T | T | T | T |
F | F | F | T | T | T |