Don’t need to do irreflexive or asymmetric 6. Consider the following relations t

Question

Don’t need to do irreflexive or asymmetric 6. Consider the following relations that are all relations on A (i.e. A ++ A) where A (a, b, c, d). Indicate which properties each relation has by circling the property names the relation possesses. a) for f(a,a), (a,b), (d,c)) o Reflexive o Irreflexive o Symmetric o Asymmetric o Antisymmetric o Transitive b) for (a,d), (d,a)) o Reflexive o Irreflexive o Symmetric o Asymmetric o Antisymetric o Transitive c) for (a,d), (a,b), (c,c)) o Reflexive o Irreflexive o Symmetric o Asymmetric o Antisymetric o Transitive d) for ((a,b), (b,a), (d,d)) o Reflexive o Irreflexive o Symmetric o Asymmetric o Antisymetric oTransitive e) for 0 o Reflexive o Irreflexive o Symmetric o Asymmetric o Antisymetric o Transitive f) for (a,c), (c,a), (c,c), (a,a)) o Reflexive o Irreflexive o Symmetric o Asymmetric o Antisymetric o Transitive

Explanation / Answer

a) As it has (a,a) hence it is reflexive

Also (a,b) is the but (b,a) is not there, hence it is antisymmetric

b) As it contains (a,b) and (b,a) objects => this is symmetric

c)

As it has (c,c) hence it is reflexive

Also (a,b) is the but (b,a) is not there, hence it is antisymmetric

Also, it is not transitive because (a,b), (a,d) => (b,d) However it is not the case.

d) It is reflexive because of (c,c)

It is symmetric because of (a,b) and (b,a)

Note: Solved first forur sub problems

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