# Valid, unsatisfied or neither? [closed]

How should I create the truth table to solve each of these questions? Maybe can give me an example?

1. $Smoke \implies Smoke$

2. $Smoke \implies Fire$

3. $(Smoke \implies Fire) \implies (\neg Smoke \implies \neg Fire)$

4. $Smoke \lor Fire \lor \neg Fire$

5. $((Smoke \land Heat) \implies ((Smoke \implies Fire) \lor (Heat \implies Fire))$

6. $(Smoke \implies Fire) \implies ((Smoke \land Heat) \implies Fire))$

7. $Big \lor Dumb \lor (Big \implies Dumb)$

8. $(Big \land Dumb) \lor \neg Dumb$

• Could you replace the image with text? Also, did you try to solve it yourself? – fade2black Sep 30 '17 at 11:23
• If you know how to construct a truth-table, this is not hard: each word is a variable and you just need to calculate what each operation does. Though, all of them are easily solved without it. – rus9384 Sep 30 '17 at 11:40
• We won't do your homework for you. Ryan's answer gives you a general method, which is actually more than you should have expected from just posting your homework online. – Raphael Oct 2 '17 at 10:07

$$F: (P \land Q) \implies \neg (P \land \neg Q)$$
$$\begin{array}{|c|c|c|c|c|c|c|c|} \hline P & Q & \neg Q & P \land Q & P \land \neg Q & \neg(P \land \neg Q) & F \\ \hline F & F & T & F & F & T & T \\ \hline F & T & F & F & F & T & T \\ \hline T & F & T & F & T & F & T \\ \hline T & T & F & T & F & T & T \\ \hline \end{array}$$