it is built from, or try to simplify the proposition using ', true], Problem 2.4: Consider the sentences shown below. 'If the Moon is made of cheese, then Homer Simpson is an alien; ' + To make it easier to translate into Propositional Logic, we can first rephrase this as It is not the case that there is a person who is both cool and funny. Although the values assigned to proposition constants are not crucial in the sense just described, in talking about Logic, it is sometimes useful to make truth assignments explicit and to consider various assignments or all assignments and so forth. Note that, for a propositional language with n proposition constants, there are n columns in the truth table and 2n rows. ['! the proposition (p ↔ q), also written Your job here is to select materials, colors, and finishes in such a way that all of the product constraints are satisfied. 'Homer Simpson is President of the U.S.A.' Of course, in some cases, it is possible to economize and do even better. The argument has two premises: The conclusion of the argument is q. A proposition p is a statement that can be true (T) or false (F). and so on. true whenever p is false, which some people find counter-intuitive. ['The Sun orbits the Earth and the Moon is made of cheese. ' Note that the constituent sentences within any compound sentence can be either simple sentences or compound sentences or a mixture of the two. )

'; writeSelectExercise(false, qCtr++, opt, aVal); The expressions on the right are the fully parenthesized versions of the expressions on the left. is always true, whether or not p and/or q are true. 'return(correct);'; The propositions are equal or '!, | and &. 'p & ( (!' There is an intimate connection between logical operations and set operations: document.writeln(startProblem(pCtr++)); ['! (if p then q), that is, "if p is true, writeTruthTableProblem(qTxt[which[1]][0], qTxt[which[1]][1]); ['*p*& !' Unary operations act on a single proposition; binary operations act on two propositions. (p1 & p2 ) → is logically equivalent to T. '3 is an odd integer', The word no here suggests a negation. ' for (k=0; k

*q*) →

*r*; !

*r*. ' '(!q) | ' + (p IFF q) and proposition (q → p). The following exercises check whether you can reduce a compound proposition document.writeln(qStr); If p and q are logically equivalent, we whichTwoByTwoTruthTable(strArr[1]) + '. Therefore,

*q*. Here is the truth table for (p → q): In logic, the proposition (p → q) is Unary operations act on a single proposition; The logical operator | is analogous to addition in arithmetic. + p, and let 'equivalent to ' + strArr[0] + ' using only ' + The subset corresponding to the proposition (p | q) combining statements that ', true], The following exercises test your ability to determine whether an Therefore, !

*p*. writeSelectExercise(true, qCtr++, opt, aVal); if (f1(truthValues[i],truthValues[j])) { The set corresponding to the proposition The subset corresponding to !p is the complement of the subset also called or and logical disjunction,