# SETS

A set is any collection or group of objects. The data that contains all objects is called the universal set (U). Each object is called a member or element () of the set. A subset () is a collection that is part of the universal set. The empty set is set that contains no objects and represented by the symbol . Two ways of defining a set: - Roster method listing the elements eg. Even number less than 10. Answer: {2, 4, 6, 8} - Set-builder notation describe the elements eg. {a, e, i, o, u} Answer: {x|x are vowels in the alphabet} Well-defined and Not Well-defined set: eg. {teachers in grade 7} Answer: Yes, because it is clear that a teacher is teaching in grade 7. {a popular basketball player} Answer: No, because some people may consider a player popular while others not. Cardinality of each set: - Number of elements in a set deals in answering the question "how many?" is a cardinal number, written n(A). - eg. A={grade 7 subjects} Answer: n(A) = 12 Finite or Infinite set: - Finite set if the set is empty or if it can be placed into a one-to-one correspondence number of elements is whole number eg. The set of weekdays - Infinite set if the set is not countable eg. The set of whole numbers Equal or equivalent sets: - Equal set if and only if they contain EXACTLY the same elements eg. A = {apple, mango} and Z = {mango, apple} - Equivalent set if and only if there is a one-to-one correspondence between the sets eg. B = {red, yellow, blue} and Y = {blue, white, black} Subset - if and only if every element of A is also an element of B - written: A B - eg. Let U = {Cyclops, Wolverine, Storm, Beast} A = {Storm, Beast} -> B = {Proffesor X, Cyclops, Wolverine} -> Proper subset - if and only if every element of A is also in B and B contains at least one element that is not in A - written: A B - eg. Let U = {Circle, Triangle, Rectangle, Square} A = {Triangle, Rectangle} -> B = {Square, Triangle, Circle, Rectangle} -> Thank you!☺️