Set Theory Using Mathematics to Classify Objects 2 © 2010 Pearson Education, Inc. All rights reserved.

The Language of Sets © 2010 Pearson Education, Inc. All rights reserved.Section 2.1, Slide Specify sets using both listing and set-builder notation Understand when sets are well- defined Use the element symbol property (continued on next slide)

The Language of Sets © 2010 Pearson Education, Inc. All rights reserved.Section 2.1, Slide Find the cardinal number of sets

© 2010 Pearson Education, Inc. All rights reserved.Section 2.1, Slide 4 Representing Sets Set – collection of objects Element – a member of a set

© 2010 Pearson Education, Inc. All rights reserved.Section 2.1, Slide 5 Representing Sets Set-builder notation: “C is the set of all x such that x is a carnivorous animal”

© 2010 Pearson Education, Inc. All rights reserved.Section 2.1, Slide 6 Representing Sets Set – collection of objects Element – a member of a set Set-builder notation:

© 2010 Pearson Education, Inc. All rights reserved.Section 2.1, Slide 7 Representing Sets A set is well-defined if we are able to tell whether any particular object is an element of the set. Example: Which sets are well-defined? (a) (b)

© 2010 Pearson Education, Inc. All rights reserved.Section 2.1, Slide 8 Representing Sets Do  and {  } mean the same thing? –  is the empty set – a set with no members –{  } is a set with a member object, namely, the empty set

© 2010 Pearson Education, Inc. All rights reserved.Section 2.1, Slide 9 Representing Sets Example: Consider female consumers living in the U.S. The universal set is

© 2010 Pearson Education, Inc. All rights reserved.Section 2.1, Slide 10 The Element Symbol Example:

© 2010 Pearson Education, Inc. All rights reserved.Section 2.1, Slide 11 Cardinal Number Example: State the cardinal number of the set.