Consider the following relations on the sets Directors $=$ D $=\{$Spielberg$,$ Scorsese,

Bigelow $\},$ Movies $=$ M $=\{$Saving Private Ryan, Lincoln, Catch Me If You Can, The Departed,

Zero Dark Thirty, Hurt Locker $\},$ Actors $=$ A $=\{$Leonardo DiCaprio, Tom Hanks, Matt Damon,

Martin Sheen, Jessica Chastain, Jeremy Renner $\}$

Consider the relation R from Directors to Movies and S from Movies to Actors.

R $=\{($Spielberg$,$ Saving Private Ryan$),($Spielberg$,$ Lincoln$),($Spielberg$,$ Catch Me If You Can$),$

$($Scorsese$,$ The Departed$),($Bigelow$,$Zero Dark Thirty$),($Bigelow$,$ Hurt Locker$)\}$

S $=\{($Saving Private Ryan, Tom Hanks$),($Saving Private Ryan, Matt Damon$),$

$($Catch Me If You Can, Leonardo DiCaprio$),($Catch Me If You Can, Tom Hanks$),$

$($Catch Me If You Can, Martin Sheen$),$

$($The Departed, Leonardo DiCaprio$),($The Departed, Martin Sheen$),$

$($Zero Dark Thirty, Jessica Chastain$),($Hurt Locker, Jeremy Renner$)\}$

This can written in shorthand as:

R $=\{($Sp$,$ SPR$),($Sp$,$ Linc$),($Sp$,$CMIYC$),($Sc$,$ Dep$),($B$,$ZDT$),($Z$,$ HL$)\}$

S $=\{($SPR$,$ TH$),($SPR$,$ MD$),($CMIYC$,$ LD$),($CMIYC$,$ TH$),($CMIYC$,$ MS$),$

$($Dep$,$ LD$),($Dep$,$ MS$),($ZDT$,$ JC$),($HL$,$ JR$)\}$

$($a$)$ What is S $$ R $($list the elements in the relation$)?$

$($b$)$ Construct T $=$ S $$ S

$1$

$.$

$($c$)$ What is T

$$

$,$ describe it in words: The relation from X to Y with $...$

$($d$)$ Calculate T

$$