Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.) (a) List all outcomes in the event A that all three vehicles go in the same direction.

Answer:a. A = {RRR,LLL,SSS}b. B = {RLS, RSL, LSR, LRS, SRL, SLR}c. C = {RRS, RRL, RSR, RLR, LRR, SRR}d. D = {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}e. C U D= {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL} C n D = {RRS, RRL, RSR, RLR, LRR, SRR}Step-by-step explanation:a.. All three vehicles go in the same directionThis means that all the three vehicles either go straight, or right or left at the same time.So, A { {RRR, LLL, SSS}b..All three vehicles take different directionsThus means that all the vehicle take different routesIf a vehicle takes the the straight direction, the other 2 vehicles take right and left directions respectivelySo, B = {RLS, RSL, LSR, LRS, SRL, SLR}c..Exactly two of the three vehicles turn rightThis means that two vehicles take right direction while the last vehicle either tske the straight route or left route.C = {RRS, RRL, RSR, RLR, LRR, SRR}d..Exactly two vehicles go in the same direction.The means that if two vehicles pass straight direction then the third vehicle takes either the right or left direction.Also, if two vehicles pass right direction, the third vehicle either takes the left direction or straight directionLastly, if two vehicles pass left direction then the third vehicle either pass the straight direction or right direction.D = {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}e. C U D = the union of items in C and D without repetitionSo,C U D= {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}C n D = Common items in C and D C n D = {RRS, RRL, RSR, RLR, LRR, SRR}List outcomes in D'.D' = List outcomes in C ∪ D.C ∪ D = List outcomes in C ∩ D.C ∩ D =