Discrete Math For the set 2 4 6 8 and the relation 2 2 4 4 6

Discrete Math

For the set, {2, 4, 6, 8} and the relation. {(2, 2), (4, 4), (6, 6)} determine whether this relation is reflexive, symmetric, antisymmetric, and transitive. (Could be multiple) Transitive Antisymmetric Reflexive Symmetric

Solution

rule of transitive :If r(a,b )and r(b,c) then r(a,c)

rule of reflexive :if r(a,a)

rule of symmetric:If relation is both transitive and reflexive,then the relation is symmetric

rule of antsymmetric:If r(a,b) and r(b,a) then a=b

In the above relation according to the rules discussed above

R is reflexive because r(a,a) or r(2,2) and r(4,4) and r(6,6)

R is antisymmetric because in r(a,b) and r(b,a) in all the relation we observe that a=b for all cases of  r(2,2) and r(4,4) and r(6,6)

but the relaton is not symmetric or transitive