Question 645502: For each of the following relations, determine whether the
relation is reflexive, symmetric, antisymmetric, or transitive.
a) ⊆ Z+ Z+ where a b if a|b (read “a divides b,”
as defined in Section 4.3).
b) is the relation on Z where a b if a|b.
c) For a given universeand a fixed subset C of, define
on () as follows: For A, B ⊆ we have A B if
A ∩ C B ∩ C.
d) On the set A of all lines in R2, define the relation for
two lines 1, 2 by 1 2 if 1 is perpendicular to 2.
e) is the relation on Z where x y if x + y is odd.
f ) is the relation on Z where x y if x − y is even.
g) Let T be the set of all triangles in R2. Define on T by
t1 t2 if t1 and t2 have an angle of the same measure.
h) is the relation on Z Z where (a, b)(c, d) if a ≤ c.
[Note: ⊆ (Z Z) (Z Z).]
6. Which relations in Exercise 5 are partial orders? Which are
equivalence relations?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Can't help you. You used symbols that don't render on other people's computers. Besides, you only get to ask one question per post. BTW 5a is one question, 5b is a second question, and so on.
John
My calculator said it, I believe it, that settles it
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