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

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 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}

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 / false: NcancelsubZ

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

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 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.

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?

State whether true or false. -|-x|=-(-x) .