Suppose S is a set of airports, and R is the following relation on S: aRb if and only if there is a direct flight from a to b. Explain your answers to the following questions and use common sense.
a. Is R reflexive? b. Is R symmetric? c. Is R transitive? d. What is the meaning of the relation R^2? Specifically, when are two airports R^2 related?
My attempt : R is not reflexive as a flight don't fly from same station to the same city. R may or may not be symmetric as a flight may be direct from a to b and not necassary from b to a. R is not transitive also.
Can any one help me with the forth part i dont know what is R^2.
So far so good. Regarding the last question, the composition of relations works as follows: if $R$ and $Q$ are two relations over the same set, then $x(Q\circ R)z$ iff there exists $y$ such that $xRy$ and $yQz$, that is in loose terms, you can go from $x$ to $z$ via $Q\circ R$ iff you can go from $x$ to some $y$ (via $R$) from which you can go to $z$ (via $Q$). In your example, $xR^2z$ iff there exists an airport $y$ to which you can fly directly from $x$, and from which you can fly directly to $z$.