For each of the following relations, determine whether the relation is reflexive

Question

For each of the following relations, determine whether the
relation is reflexive, symmetric, antisymmetric, or transitive.

a) ""R %u2286 Z+ Z+ where a "R" b if a|b

b) "R" is the relation on Z where a "R" b if a|b.

c) For a given universeand "U" a fixed subset C of "U", define
"R" on "P"("U") as follows: For A, B %u2286 "U" we have A "R" B if
A %u2229 C B %u2229 C.

d) On the set A of all lines in R2, define the relation "R" for
two lines L1, L2 by L1 RL2 if L1 is perpendicular to L2.

e) "R" is the relation on Z where x "R" y if x + y is odd.

f ) "R" is the relation on Z where x "R" y if x - y is even.

g) Let T be the set of all triangles in R2. Define "R" on T by
t1 t2 if t1 and t2 have an angle of the same measure.

h) is the relation on Z x Z where (a, b)"R"(c, d) if a %u2264 c.
[Note: "R" %u2286 (Z x Z) X (Z x Z).]

Note: The "R" or "P" or "U" letter should look like they are written is cursive, could not properly copy them.

Explanation / Answer

(1)reflexive,anti symmetric,transitive...........

(2)reflexive,anti symmetric,transitive.............

(3)reflexive,symmetric,transitive.........

(4)symmetric.......

(5)symmetric,...

(6)reflexive,symmetric,transitive.....

(7)question is not clear......

(8)reflexive,,,antisymmetric,transitive...

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