(a) Let A, B, and C be finite sets in some universe U. Prove that

|AuBuC| =

|A| + |B| + |C| – |AnB| – |AnC| – |BnC| + |AnBnC|

where ‘n’ means INTERSECTION and ‘u’ means UNION.

(b) How many numbers between 1 and 100(inclusive) are not divisible by 2,3 or 5.

(c) graph the function f(x) = topceiling[x] – bottomceiling[x] on the interval [-3,3].Applied Mathematics split very broadly into three main categories: Statistics, Mechanics and Modelling

Careers in Statistics include Market Analysis, Risk Analysis, Trend Analysis and various research and development branches involved in Bayesian Mathematics such as image and speech recognition.

Careers in Mechanics include materials research and development, Ballistics and, Mechanical design and testing for the car and avionics industries.

Carrers in Mathematical Modelling involves breaking real life problems down to algoriths that can be modelled for further analysis or development. Careers include UML Computing.