Learn set notation. Set notation is a precise way to show what belongs or does not belong in a group. For example, let's define set A to include the numbers 1, 2, 3, 4 and 5. In set notation, we would write A = {1,2,3,4,5}, or more precisely, A = {x is an integer: 0 < x < 6}. The expression "x is an integer: 0 < x < 6" is another way of saying x is an integer such that x is larger than zero and less than six.
Construct Venn diagrams to visually demonstrate sets and their operations. If you have two sets A and B, a Venn diagram of A and B will illustrate each set as a circle. If A and B share objects or elements, then their circles will interlock and have a common central space where the shared elements reside.
Color your Venn diagrams. Colors provide a fantastic visual aid for understanding set operations. An alternative to coloring is to use computer software that colors set operations for you.
Use flashcards to memorize standard sets. Standard sets are used frequently in exercises and proofs; the ability to recall them quickly saves time and crucial test points. They include
N - natural numbers: {1, 2, 3, 4, 5, ...};
N^0 - non-negative integers: {0,1,2,3,4,5, ...};
Z - integers: {... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...};
Q - rational numbers, or numbers that can be written as x/y, where y is not 0, such as -1.444 or 3/4; and
R - real numbers, or any number on the number line, such as -1, 0, 3.5 and 7.
Use one flashcard for each set. On one side of the flashcard, write the letter that identifies the set, such as N, Z or Q. On the other side of the flash card, write the definition of the set along with some examples of numbers in the set. Test yourself by looking at one side of the flashcard and recalling the details on the other side.
Write down the meaning of set identities using words. There are many laws in set theory, including identity laws, domination laws, idempotent laws, the complementation law, commutative laws, associative laws, distributive laws and De Morgan's laws. These laws will be easier to understand and remember if you use common language to express them. For example, one of the identity laws says that the union of set A with the empty set is equal to set A. In everyday language, this law says that if you take all the objects in set A and combine them with no other objects, you still get just the objects of A.