1 / 16

Sets: An introduction

Sets: An introduction. Coming up… Probability. In our study of probability, two things will be of great use to us: our understanding of set operations our counting ability. Definition. A set is a well-defined collection of objects, called elements. Remark:

rayya
Download Presentation

Sets: An introduction

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Sets: An introduction

  2. Coming up… Probability • In our study of probability, two things will be of great use to us: • our understanding of set operations • our counting ability

  3. Definition A set is a well-defined collection of objects, called elements. Remark: Not every collection of objects is a set. There must be a definite way of telling what is and what is not in the set.

  4. Example #1 Determine which of the following collections are sets. 1.The collection of states in the US. 2.The collection of great US presidents.

  5. Set Representation We consider 3 ways of defining a set. • A set may be defined by listingits elements. For instance, the set A of letters in the word “beloved” may be written as A = {e, b, l, o, d, v} Sets are often named with capital letters. Order of elements doesn’t matter; no duplicates.

  6. 2. A set may be defined by describinga common feature of all of itselements. For instance, consider the set B given by B = {x | x is a positive integer less than 5} This is read: “x such that x is a positive integer less than 5” Clearly, the elements of B are 1, 2, 3, and 4.

  7. 3. A set may be defined by drawinga Venn diagram. For instance, the set C may be represented by the circle shown below inside a rectangle. C

  8. Example #2 • Find the set of all the possible outcomes: • when you flip a penny. • when you toss a die.

  9. a) Let A be the set of the possible outcomes when you flip a penny. Then A = {h, t}. b) Let B be the set of the possible outcomes when you toss a die. Then B = {1,2,3,4,5,6}.

  10. Set Operations Intersection The intersection of two sets A and B is the set of elements that are in both sets. It is denoted by A ∩ B.

  11. Union The union of two sets A and B is the set of all elements of A or B. It is denoted by A U B. B A

  12. If every element of a set A is also an element of a set U, then say that A is a subset of U. For instance, the set A = {b, e, t} is a subset of the set U = {b, e, a, s, t}.

  13. Complement of a Set Let A be a subset of U. Then we define the complement of A in U as the set of all elements of U not in A. It is denoted by A'. A U

  14. Remarks: • The set with no element is called the empty setand is denoted by • The number of elements in a set A is denoted by n (A). • A set may be • finite, like the set of letters of the English alphabet or • infinite like the set of positive whole numbers.

  15. Example #3 Given the sets: U = {h, i, m, e, a, t, l, o, v, r, s} A = {m, a, t, h} B = {h, a, t, e} C = {l, o, v, e} Find: 1) B ∩ C 2) A U B 3) n(U) 4) B’ 5) A ∩ C 6) n(A ∩ C)

More Related