{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# dm-lec1-sets-p - Sets Sets and Logic Chapter 1(1.1 Sets...

This preview shows pages 1–2. Sign up to view the full content.

Sets and Logic Chapter 1 (1.1 Sets) September 2, 2009 Sets A set is a collection of objects, d i t t k i t t order is not taken into account. Objects = elements members Objects = elements, members How to describe it? By listing all members: A = {1 2 3 4} – By listing all members: A = {1,2,3,4} – By listing a property necessary for membership: B = {x | x is a positive, even integer} – Symbol: [email protected] 2 CS204 Discrete Math (Fall 2009) Sets Element C Cardinality If X is a finite set, we let |X| = number of elements in X • Example: what is the cardinality of the set {R,Z} =? Membership Membership Empty (or null or void) set, Two sets X and Y are equal: X=Y For every x, if x X, then x Y, and for every x, if x Y, then x X. Subset A B Subset A Proper subset A B Power set: set of all subsets (proper or not) of a set X [email protected] 3 CS204 Discrete Math (Fall 2009) Sets Power set If |X| | | 2 n If |X| = n, | | = 2 – Formal proof in Section 2.4 Set operations – Union Union – Intersection

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}