Problem: You are going to buy (B) at most 3 rental properties - call them 'a', 'b', and 'c'. You estimate that property a will generate $1000 of income, property b will generate $800 of income, and property c will generate $600 of income. Due to bizarre local tax laws, if you purchase more than one property, your income will be the average of the incomes from the properties that you purchase. (For example, if you purchased b and c, then your income would be the average of $800 and $600, or $700.) You can purchase at most two properties. Furthermore, if you purchase property b, then neither a nor c may be purchased.
(a) Write down a wff in TFL that represents each of the constraints on your choice.
(b) Are there any additional numerical constraints on your choice? If so, what are they?
(c) Make a joint truth table for the wffs that you wrote down in part (a).
(d) Which property or properties should you purchase, assuming that you want to maximize estimated income?