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

Chapter 1, Problem 13

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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 presentedthe truth table for the inclusive or, whose meaning is one or the otheror both. The exclusive or, meaning one or the other but not both anddenoted , has its uses in English, as in She will marry Heckle or shewill marry Jeckle. The inclusive or is much more useful in mathematicsand 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 flashmemory chips. A NAND B is defined to be the negation of A and B. ANOR 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).