(Solved): Here are two relations defined on the set {a, b, c, d}:S = { (a, b), (a, c), (c, d), (c, a) }R = { ( ...

1. Here are two relations defined on the set {a, b, c, d}:
   • S = { (a, b), (a, c), (c, d), (c, a) }
   • R = { (b, c), (c, b), (a, d), (d, b) }

Write each relation as a set of ordered pairs.

1. S ο R = {(b, d), (b, a)}
2. R ο S = {(a, c), (a, b), (c, b), (c, d)}
3. S ο S = {(a, d), (a, a), (c, b), (c, c)}
   
   For each relation, indicate whether the relation is:
   • reflexive, anti-reflexive, or neither

Answer: S = anti-reflexive

R = anti-reflexive

S ο R = anti-reflexive

R ο S = anti-reflexive

S ο S = neither

• symmetric, anti-symmetric, or neither

Answer: S= neither because of the (a, c), (c, a) in there

R = neither because of the (b, c), (c, b) in there

S ο R = anti-symmetric

R ο S = anti-symmetric

S ο S = anti-symmetric

• transitive or not transitive
  Answer this part for me, please. Thank you