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Matrices help!

  • 27-08-2010 2:58am
    #1
    spa21788
    Closed Accounts Posts: 5 ✭


    I have a question due and I have no idea how to do it! Any help please??!?!?!?


    Let R be the relation on {a,b,c,d} defined by the following matrix:

    a b c d

    a ( T F T F )
    b ( F T T F )
    c ( F T T F )
    d ( F F F T )

    a.) Show R
    b.) Draw the graphical representation of R
    c.) State, giving reasons, whether R is reflexive, symmetric or transitive.


    I think c.) is symmetric because rows = columns but I have no idea what to do otherwise! :(
    Tagged:


Comments

  • #2
    Fremen
    Registered Users, Registered Users 2 Posts: 2,481 ✭✭✭Fremen


    I'm not really sure what's meant by "Show R", you may have to help out on that one.

    For part b, draw four dots and label them a,b,c and d. Link two dots a and b, say, with an arrow if the entry (a,b) reads true, otherwise don't link them.

    For part c, a reflexive relation means for all entries x, (x,x) reads true. Does this hold for your example?

    A symmetric relation means that (x,y) has the same value as (y,x). Again, check whether this holds.

    A transitive relation means that if (z,y) is true, and (y,z) is true then (x,z) has to be true. From your graph, you will be able to check if this holds.


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