Question

Find the dual of each of these compound propositions.

a)$p\vee \neg q$

b)$p\wedge (q\vee (r\wedge T\left)\right)$

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

Short answer

a)$p\wedge \neg q$

b)$p\vee (q\wedge (r\vee F\left)\right)$

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

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 $\vee$ by $\wedge$ , each T by F, and each F by T.

Dual of a)

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

Dual of b)

Dual of $p\wedge (q\vee (r\wedge T\left)\right)$ is .$p\vee (q\wedge (r\vee F\left)\right)$

Dual of c)

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