Chapter 1.1, Problem 14E

Other logical connectives between two propositions P and Q are possible.

14. “NAND” and “NOR” circuits are commonly used as a basis for flash memorychips. A NAND B is defined to be the negation of “A and B.” A NOR B isdefined to be the negation of “A or B.”
(a) Write truth tables for the NAND and NOR connectives.
(b) Show that $(A\text{NAND}B)\vee (A\text{NOR}B)$ is equivalent to $(A\text{NAND}B).$
(c) Show that $(A\text{NAND}B)\wedge (A\text{NOR}B)$ is equivalent to $(A\text{NOR}B).$