Chapter 12.1, Problem 39E

In Exercises 35-42, use the laws in Definition 1 to show that the stated properties hold in every Boolean algebra.

39. Show that De Morgan’s laws hold in a Boolean algebra. That is, show that for allxandy, $\overline{\left(x\vee y\right)}=\bar{x}\wedge \bar{y}$ and $\overline{\left(x\wedge y\right)}=\bar{x}\vee \bar{y}$ .