Show that the relation `R={(a,b) : a,b in N and a|b}` is not an equivalence relation in N where `a|b` means that a is a divisor of b.

State true or false: R= {(a,b) : a,b in N , a+b>0} is an universal relation in N.

Is the relation R={(A,B) : A,B in P(S) and AsubB} an equivalence relation in the power set P(S) where S is a non-empty set?

Show that the intersection of two equivalence relations in a set is again an equivalence relation in the set

Show that the relation R in the set of integers given by R={(a,b):4" divides "a-b} is an equivelence relation. Find the set of all elements related to 0.

State true or false: R= {(a,b) : a,b in A, ab=100} is an empty relation in the set A={ x : x in N, x<10}

Is the relation R={(a,b),(b,a)} on the set {a,b,c} reflexive ?

State true or false: R={(a,b) : a,b in A, |a-b| <5} is an universal relation in the set A={x : x in R, -50

Prove that the intersection of two equivalence relations in a set is an equivalence relation and give an example to show that the union of two equivalence relations in a set is not necessarily an equivalence relation.

State true or false: R={(a,b) : a+b=5} is an empty relation in the set of whole numbers.