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.