Question

Consider following relation on set (1, 2, 3, 4, 5, 6}
R= {(i,j) | |i-j|=2}
Is R transitive?
Is R reflexive?
Is R symmetric?

Answer 1

$R= \begin{vmatrix} 0 & 0&1&0&0&0 \\ 0&0&0&1&0&0\\ 1&0&0&0&1&0\\ 0&1&0&0&0&1\\ 0&0&1&0&0&0\\ 0&0&0&1&0&0 \end{vmatrix}$

$\forall a,b,c :aRb\land bRc \implies \neg (aRc)$

Antitransitive

$\forall x: \neg(xRx)$

Antireflexive

$\forall a,b: aRb\implies bRa$

Symmetric