Question

Find the dual of each of these compound propositions..

a)$p\wedge \neg q\wedge \neg r$

b)$(p\wedge q\wedge r)\wedge s$

c)$(p\vee F)\wedge (q\vee T)$

Short answer

a)$p\vee \neg q\vee \neg r$

b)$(p\vee q\vee r)\vee s$

c)$(p\wedge T)\vee (q\wedge F)$

Step-by-step solution

Step1:Definition of dual

The dual of a proposition which contains only the logical operators $\vee ,\wedge ,\neg$, is the compound proposition obtained by replacing each $\wedge$by $\vee$ , each $\wedge$by $\vee$, each $\mathbf{T}$by , $\mathbf{F}$and each $\mathbf{F}$ by $\mathbf{T}$

Dual of a)

Dual of $p\wedge \neg q\wedge \neg r$is .$p\vee \neg q\vee \neg r$

Dual of b)

Dual of $(p\wedge q\wedge r)\wedge s$ is$(p\vee q\vee r)\vee s$

Dual of c)

Dual of $(p\vee F)\wedge (q\vee T)$is $(p\wedge T)\vee (q\wedge F)$