Question

Consider the binary relation: R = {(x, y), (x, z), (z, x), (z, y)} on the set {x, y, z}. Which one of the following is TRUE?

• A. R is symmetric but NOT antisymmetric
• B. R is NOT symmetric but antisymmetric
• C. R is both symmetric and antisymmetric
• D. R is neither symmetric nor antisymmetric
  

Answer 1

The correct option is D R is neither symmetric nor antisymmetric


Given R = {(x, y), (x, z), (z,x), (z, y)} on set {x, y, z} here (x, y ) $ϵ$ R and (y, x) $\text{/}ϵ$ R.
$\therefore$ R is not symmetric
Also (x, z) $ϵ$ R and (z, x) $ϵ$ R
$\therefore$ R is not antisymmetric.
R is neither symmetric nor anti-symmetric.