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| <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 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, a-b=2} is neither an empty relation nor a universal relation in the set A={0,1,2,3,4,5}

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.

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

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

State whether true or false. (-x)|x|=x^2 .

State whether the following relations are reflexive, symmetric and transitive: R={(x,y) : x,y in A} x and y work at the same place. R={(x,y) : x,y in A} x is son of y. in the set A of all employees of ASEB.