a tautology

a contingency

a contradiction

equivalent to $\mathrm{p} \vee \mathrm{q}$

The lamp is always on

The lamp is always off

Symbolic form is $\mathrm{p} \vee(\sim \mathrm{p} \wedge \sim \mathrm{q}) \vee \mathrm{q}$

is equivalent to $\mathrm{p} \vee \mathrm{q}$

$(-q \wedge p) \wedge(p \wedge \sim p)$

$(p \wedge q) \wedge(\sim p \wedge q)$

$[(\sim q) \wedge p] \wedge q$

$(\sim q \wedge p) \vee(p \vee \sim p)$