In this task, you need to provide the correct option for a given problem from the provided options.

[Q]: Problem: set a consists of the integers from 4 to 17 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ? 
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 12
[A]: e


[Q]: Problem: of the 65 cars on a car lot , 30 have air - conditioning , 45 have air bag , and 12 have both air - conditioning and air bag . how many of the cars on the lot have neither air - conditioning nor air bag ? 
Options: a ) 2 , b ) 8 , c ) 10 , d ) 15 , e ) 18
[A]: c


[Q]: Problem: the ratio of the incomes of a and b is 2 : 3 and the ratio of their expenditure is 1 : 2 . if at the end of the year , each saves $ 500 then the income of a is ? 
Options: a ) $ 1000 , b ) $ 1500 , c ) $ 1200 , d ) $ 900 , e ) $ 1100
[A]:
a