Other logical connectives between two propositions P and Q are possible. (a) The word or...

Other logical connectives between two propositions P and Q are possible. (a) The word or is used in two different ways in English. We have presented the truth table for the inclusive or, whose meaning is “one or the other or both.” The exclusive or, meaning “one or the other but not both” and denoted has its uses in English, as in “She will marry Heckle or she will marry Jeckle.” The “inclusive or” is much more useful in mathematics and is the accepted meaning unless there is a statement to the contrary.

(i) Make a truth table for the “exclusive or” connective .

(ii) Show that is equivalent to

(b) “NAND” and “NOR” circuits are commonly used as a basis for flash memory chips. A NAND B is defined to be the negation of “A and B.” A NOR B is defined to be the negation of “A or B.”

(i) Write truth tables for NAND and NOR connectives.

(ii) Show that (A NAND B) (A NOR B) is equivalent to (A NAND B).

(iii) Show that (A NAND B) (A NOR B) is equivalent to (A NOR B).