{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

relations and functions

# relations and functions - Relations and Functions LING 178...

This preview shows pages 1–3. Sign up to view the full content.

9/4/2007 1 Relations and Functions LING 178 Relations A RELATION holds between two or more ordered entities. 2 is greater than 1 aardvark comes before anteater Homer is the father of Bart everyone admires Madonna Ordering is important. We cannot change the order without changing the meaning. Relations and ordering A set of two elements is a PAIR. The elements are not ordered. {1, 2} = {2,1} A set of two ordered elements is an ORDERED PAIR and is used to represent a relation. <1,2> <2,1> When there is a relation between one object and several other different objects, we list the relationships as separate pairs. <Homer, Bart> <Homer, Lisa> <Homer, Maggie>

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

View Full Document
9/4/2007 2 Cartesian Product The CARTESIAN PRODUCT of two sets, A and B, is the set consisting of all ordered pairs formed by combining one element of A with one element of B. A x B = { <x,y> | x A and y B } A = {a, b, c} B = {1,2} what is A x B? a b c 1 2 A x B = { <a,1>, <a,2>, <b,1>, <b,2>, <c,1>, <c,2>} Is the following true? A x B = B x A What is B x B? Functions When we relate two sets of elements in such a way that every element of set A is paired with just one element of set B, we have a FUNCTION. Formally, a relation R from A to B is a function iff Each element in the domain [A] is paired with just one element in the range [B].
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern