Question

Let r be a relation over the set nxn and it is defined by (a, b) r (c, d) a+d=b+c. Then r is

Answer 1

Answer:

intransitive relation

Step-by-step explanation:

relation : (a, b) r (c, d) a+d=b+c

now....

reflexivity : (a, a) r (a, a) = a +a = a + a ; (a, a) € r

symmetry : (a, b) r (c, d) a+d=b+c & (b,a) r (d,c) , b+c = a +d ; (a, b), (b,a) € r

transitivity : (a, b) r (c, d) a+d=b+c

& (c, d ) r (e, f) = c+f = d + e but : (a, b) not r (e, f)

hence...for (a,b) (b,c)...(a,c) €(not) r

therefore....it's intransitive relation