Decide whether each of the following
sentences is valid, unsatisfiable, or neither. Verify your decisions
using truth tables or the equivalence rules of
Table logical-equivalence-table (page logical-equivalence-table).
-
${Smoke} {:;{\Rightarrow}:;}{Smoke}$ -
${Smoke} {:;{\Rightarrow}:;}{Fire}$ -
$({Smoke} {:;{\Rightarrow}:;}{Fire}) {:;{\Rightarrow}:;}(\lnot {Smoke} {:;{\Rightarrow}:;}\lnot {Fire})$ -
${Smoke} \lor {Fire} \lor \lnot {Fire}$ -
$(({Smoke} \land {Heat}) {:;{\Rightarrow}:;}{Fire}) {;;{\Leftrightarrow};;}(({Smoke} {:;{\Rightarrow}:;}{Fire}) \lor ({Heat} {:;{\Rightarrow}:;}{Fire}))$ -
${Big} \lor {Dumb} \lor ({Big} {:;{\Rightarrow}:;}{Dumb})$ -
$({Big} \land {Dumb}) \lor \lnot {Dumb}$