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 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.

Is the relation R={(L_1, L_2) : L_1,L_2 in L} and L_1 is perpendicular on L_2 an equivalence relation in the set L of all straight lines in the coordinate plane?

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

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.

Show that the relation R in the set Z of integers given by R{(x,y):6" divides "x-y} is an equivalence relation. Find the set of all elements related to 0.

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

Write the relation between power P, work done W and time t.

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

Let L be the set of all lines in the XY - plane and R be the relation in L defined by R={(l_(i)l_(j))|l_(i)" is parallel to "l_(j)l_(i)AA_(i),j} . Show that R is an equivalence relation. Find the set of all lines related to the line y=7x+5