Introduction to Logic

Exercise 2.3 - Evaluation

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 shows a typical order form for the company's 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 following sentences are constraints that characterize the possibilities. Your job here is to select a truth value for each constraint indicating whether that constraint is satisfied by the order shown above.

a. aluminumcopperiron
b. aluminumgrey
c. copper ∧ ¬coatedred
d. coated ∧ ¬coppergreen
e. greenblue ⇔ ¬textured ∧ ¬iron