Given the following relations, tell if each relation is reflexive, symmetric, antisymmetric or transitive.

a) R is over Z where R = { (x,y) | x > y }

b) R is over { 1,2,3,4,5,6 } where R = { (3,5), (4,5) }

c) R is over {living humans} where R = { (x,y) | x and y are biological sisters with the same parents } . (Note: no woman is her own sister).

d) R is the relation over the set of lines in a plane where (x, y) in R if x and y are perpendicular.

e) R is over {speaking humans} where R = { (x,y) | x and y speak a common language }

f) R is over { real numbers } where R = { (x,y) | x*y 10 }