For each of these activities pages, you will find detailed instructions how to use the page under the Instructions button on that page.

The Set Constructor is the first place you go to build new sets for use throughout this Microworld. Later, in the Workshop, you may build sets more conveniently, but this is the place to start.

The Set Viewer is a place to view simple sets. Each set will have a name. 16 sets are predefined for you. They have the names: mammal, aquatic, lays_eggs, reptile, bird, hunts, snake, has_horns, feline, canine, primate, has_tusks, ungulate, fruit_eater, quadruped, and has_fur. As you create new sets, first in the Constructor, and later by command, using set operations and relations, new sets will be named: an1, an2, ... The sets of animals that you work with on projects may be saved to disk and later restored. In the Set Viewer, you may see the animals of any set that you name as colorful pictures.

The Operations Lab is the place to begin experimenting with the basic operations on sets: Union, Intersection and Complementation. These operations are discussed in the Reading "Operations on Sets." There you may use the Show command to show pictures of sets obtained by combining old sets using these operations, the Build command to create new sets in this way, the Size Command to tell the size of any set, and the IsEqual and Subset commands to compare sets.

The Relation Viewer is the first and simplest place to define and view relations between sets, and functions between sets. Here, you choose two sets: a Source set and a Target set, and define any relation or function from Source to Target. The properties of relations and functions are discussed in several of the readings, notably, "Algebra of Relations," and "Composition of Functions" and while the algebraic manipulation of these is best done in the Workshop, here you may create and view them with pictures. Like Sets, each relation and function created in the Microworld has a name such as: re1, re2,.. and these may also be saved to disk and later restored.

The Workshop and Office have similar functions. The Workshop is more graphical, and the Office more text-oriented. In these environments, you may use the Show command to show Sets, Relations, the results of operations on sets, the results of algebraic operations (such as composition and inversion) on relations or functions, the images and preimages of relations between sets, the effects of permutations (as invertible functions) and so on, interactively. You may use the Build Command to create new sets and relations by any combination of the mentioned operations. You may test sets so constructed for equality or for subsets. We also explore in the Workshop the structure of elementary groups, such as dihedral groups, the properties of ordering and equivalence relations, and the notion of cardinality.

Finally, the Set Safari Game brings it all together with an amusing exploration of the relations between set operations and the propositional calculus of logic. The rules of the game are simple (but described in more detail there). The computer creates a "hidden" set of animals, telling you its size only. It creates this set by generating randomly a proposition from the primitive 16 proposition-sets listed above. Such a proposition might be: "the union of all reptiles and animals that both hunt and are not quadrupeds" This is a definite set, and the computer can generate 2^17 such propositions randomly (over 100,000). This corresponds to a somewhat smaller number of actual sets (There are 2^46-1 sets possible).

The player then proposes propositions, such as: "the intersection of mammals and animals that do not hunt" The computer replies by informing the player of the number of animals in its set that satisfy the proposition. Using this information, the player proceeds to the next guess. If the player's proposition produces the identical set, the computer congratulates the player, and then shows its proposition and the set it produced. The player may of course use any of the commands (Show, Build, Subset, IsEqual and Size) to help her along. Often, with care, the player can find the precise set within 10 guesses, but the propositions are seldom identical.

The reasoning employed is, of course, precisely the reasoning that we formalize and develop in the readings, and so this exercise is a useful accompaniment to the course of readings.