Introduction to Logic

Exercise 2.5 Satisfaction

A small company makes widgets in a variety of constituent materials (aluminum, copper, iron), colors (red, green, blue, grey), and finishes (matte, textured, coated). The box below is the company's order form for widgets.

Order Form
Material Aluminum Copper Iron
Color Red Green Blue Grey
Finish Matte Textured Coated

Although there are more than one thousand possible combinations of widget features, the company markets only a subset of the possible combinations. The sentences in the following table lists some constraints that characterize the possibilities together with an indication of whether they are satisfied by the order depicted on the order form. As you change the form, the truth values of these sentences are recomputed and displayed in this table.

SentenceTruth Value
aluminum | copper | iron
red | green | blue | grey
aluminum => grey
copper & ~coated => red
iron => coated

Your job here is to fill in the order form in such a way that all of the product constraints are satisfied. Note that there are multiple ways this can be done.