Question

Which of the following statements is not correct for the relation R defined aRb, if and only if b lives within one kilometre from a?

• A. R is reflexive
• B. R is symmetric
• C. R is not anti-symmetric
• D. None of the above

Answer 1

Answer: (C)

R is not anti-symmetric

$(a,a)ϵR$ R is reflexive

$(a,b)ϵR\Rightarrow a$ lives within one kilometer from b

$\Rightarrow b$ lives within one kilometer from a

$\Rightarrow bRa$

$\therefore (a,b)ϵR\Rightarrow (b,a)ϵR$

$\therefore R$ is symmetric

$\therefore R$ is anti symmetric

because $(a,b)ϵR$ & $(b,a)ϵR$

and $a\ne b$