SIMPLE AND COMPOUND PROPOSITIONS
Recall from Chapter 5 that, in logic, a proposition is something that evaluates unequivocally to either TRUE or FALSE. Here are some examples:
2 + 3 = 5
2 + 3 > 7
Jupiter is a star
Mars has two moons
Venus is between Earth and Mercury
Of these, Nos. 1, 4, and 5 are true and Nos. 2 and 3 are false—though we do need to be rather careful in the case of No. 5 over what exactly we mean by “between”! (To be a little more precise about the matter, what I mean by it is this: If we denote the distances of Mercury, Venus, and Earth from the sun by m, v, and e, respectively, then m < v < e.) Be that as it may, a good informal test for whether something, p say, is a valid proposition is to ask whether “Is it true that p?” is a sensible question. For example, “Is it true that 2 + 3 > 7?” is certainly a sensible question, even though the answer is no. To check your understanding of this point, which of the following do you think are legal propositions? (You might want to check the answers in Appendix F before continuing with this chapter.)
Bach is the greatest musician who ever lived.
What’s the time?
Supplier S2 is located in some city, x.
Some countries have a female president.
All politicians are corrupt.
Supplier S1 is located in Paris.
We both have the same favorite author, x.
Nothing is heavier than lead.
It will rain tomorrow.
Supplier S6’s city is unknown.
By the way, there’s a very fine point here (which I’m mostly going to ignore; I mention it only to head off at the ...