Qn 1.

Let A={1,2,3,4}

a) Check whether the following relation R={(1,1),(2,2),(3,4)(4,2)} is reflexive, symmetric or transitive.

b) Write an equivalence relation on A with minimum number of elements.

c) Show that a relation on A having 5 elements cannot be an equivalence relation.

Qn 2.

Let A= {1,2,3,4,5,6} and R is a relation on A as R={(x,y): y divides x}

a) Show that R is reflexive and transitive, but not symmetric

b) Write another set B with 4 elements on which the above relation R is an equivalence relation.