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

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}

State true or false: R={(a,b) : a,b in A, a-b=2} is neither an empty relation nor a universal relation in the set A={0,1,2,3,4,5}

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

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

State true / false: NcancelsubZ

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 Cube of any odd number is even.

Given an example of an empty relation in the set A={1,2,3,4} .

State whether the following relations are reflexive, symmetric and transitive: R={(a,b) : a,b in Z and a+b is even } in the set of integers, Z.