1.consider the ffg relation on A where A={1,2,3,4,5,6,,8}

aRb if and only if a/b < min(a,b)

ie. if a divided by b is smaller than the minimum of a and b. eg sR8 since 2/8=1/4 and min(8,2)=2 and 1/4<2

a)Draw the directed graph of R

b)Give all the paths of lenghts 2 from 3.

c)Give the domain and range of R

d)Determine R(4)

e)Write Mr and use it and Boolean multiplication to find R SQUARED

f)Use Mr to find all pairs joined by paths of length 3.

gUse R squared to decide whether R is transitive.

h) Use Warshalls algorithim to find the transitive closure of R.

2.Decide using the definition or matrix of R whether R of question 1 is:

a)reflexive

b)irrreflexive

c) symmetric

d)asymmetric

e)antisymmetric

f)transitive

Give reasons for your answers.