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- March 16th 2013, 08:07 AM #1

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## problem..

Determine whether the relation R on the set of all Web pages is reflexive,symmetric,antisymmetric, and/or transitive,where(a,b) belongs to real number if and only if...

a) everyone who has visited web page*a*has also visited web page*b.*

b) there are no common links found on both web page*a*and web page*b.*

c) there is atleast one common link on web page*a*and web page*b.*

d)there is a web page that includes links to both web page*a*and web page*b.*

- March 16th 2013, 09:25 AM #2

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- March 16th 2013, 11:48 AM #3

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- March 16th 2013, 11:59 AM #4

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## Re: problem..

Determine whether the relation R on the set of all Web pages is reflexive,symmetric,antisymmetric, and/or transitive,where(a,b) ∈ R if and only if...

a) everyone who has visited web page a has also visited web page b.

b) there are no common links found on both web page a and web page b.

c) there is atleast one common link on web page a and web page b.

d)there is a web page that includes links to both web page a and web page b.

- March 16th 2013, 12:08 PM #5

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## Re: problem..

Good for you for removing the reference to the set of real numbers, which meant that you didn't understand the question at all. I have already started writing a scathing reply about this.

Now, if you know the definitions of these types of relations (reflexive and so on), you should be able to answer at least some questions. Show your work so that we can have an idea of what you understand, and please describe what difficulties you are having answering other questions. For example, you probably realize that everyone who has visited web page a has also visited web page a, so the relation from a) is reflexive.

- March 16th 2013, 12:23 PM #6

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- March 16th 2013, 12:37 PM #7

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## Re: problem..

The clauses a) through d) define four binary relations on the set of web pages. Each relation is denoted by R. Given two web pages, a binary relation says whether they are related in a certain way. In other words, a binary relation is a function from pairs of web pages to the set {True, False}; it takes two pages and says yes or no. A binary relation can also be thought of as the set of those pairs of pages for which the answer is yes.

The beginning of the question lists several properties of relations (reflexive and so on). You need to look them up in your source (textbook or lecture notes). It is generally not a good idea to explain these definitions on this forum for every new question because these definitions are well-known and have been described and explained elsewhere better than it is possible here. Besides, if you don't read your textbook, you won't have the necessary explanations and examples to solve problems anyway.

The question asks if these four relations have the four listed properties.

- March 16th 2013, 12:38 PM #8

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## Re: problem..

reflexive: is it true that everyone who visited web page a also visited web page a?

symmetric: if every one who visited web page a also visited web page b does it follow that everyone who visited web page b visited web page a?

anti-symmetric." If every who visited web page a also visited web page b, does it follow that there MUST be someone who visited webpage b but did not visit web page a?

transitive: if every one who visited web page a also visited web page b,**and**every one who visited web page b also visited web page c, does it follow that everyone who visited web page a also visited web page c?

Now you try the others. This is the second time you have posted problems on relations. Surely you must know what "reflexive", "symmetric", "anti-symmmetric" and "transitive" mean!

b) there are no common links found on both web page a and web page b.

c) there is atleast one common link on web page a and web page b.

d)there is a web page that includes links to both web page a and web page b.i didn't understand the whole question... could you please describe the whole question in detail.... it's so confusing....

thanks**definitions**of "reflexive", "symmetric", "anti-symmetric", and "transitive". Surely they are in your text box? Look them up!