An airline keeps information about its passengers and has noted the following facts about the services it supplied between London and Singapore during a particular week. The airline only operated two different types of aircraft, which they denote byAandZ.

(a)Travellers onZ always have excess baggage,X, whereas travellers onA sometimes do not.

(b)Smokers,S, always travel onAand always have excess baggage.

(c)There is no Executive Class,E, travel onZ.

(d)Businessmen,B, always travel Executive Class and never smoke.

(e)Passengers requesting champagne,C, are always businessmen and never have excess baggage.

Question 1

Interpret each of the above statements (a) to (e) in set notation, and hence construct a single Venn diagram to illustrate the relationships betweenA,B,C,E,S,XandZ.

The following additional quantitative data are available for the week and route in question.

• 40% of all travellers on the airline used typeZ aircraft.
• Only 20% of all travelling businessmen did not request champagne.
• Businessmen make up 80% of all the Executive Class travellers.
• 150 smokers travelled with the airline. This represents 10% of all the travellers.
• There were 160 passengers who requested champagne.

What is the minimum and maximum number of non-smoking, non-Executive Class travellers onA

Aaircraft?

(The number of elements in a set is called theorderof the set and is denoted byn(). For example, we haven(C)=160andn(S)=150.)