Logic For Dummies, 2nd Edition

Chapter 13

Putting Operators in Their Place

IN THIS CHAPTER

Recognizing the sufficiency of the SL operators

Creating SL statements with fewer than five operators

Appreciating the Sheffer stroke

In Chapter 4, I explain that the word or has two different meanings in English: The inclusive or means “either this or that, or both,” whereas the exclusive or means “either this or that, but not both.” I also note that the or-operator in sentential logic (SL) removes this ambiguity because it always represents the inclusive or. At the time, you may have thought this was highly unfair and discriminatory. In fact, the more rebellious among you may have considered starting a movement to add a sixth operator to SL.

But, before you take to the streets carrying homemade signs and chanting, “Two, four, six, eight, the exclusive or is really great,” read this chapter. In these pages, you find out how the exclusive or — as well as any other homemade operator you may come up with — is already covered by the five SL operators. In fact, in this chapter, I show you how these five symbols allow you to express any possible truth function you care to devise.

You also discover how you can express any possible ...