State and prove the principle of inclusion-exclusion. Use it to calculate , where is Euler's -function.
In a certain large college, a survey revealed that of the fellows detest at least one of the pop stars Hairy, Dirty and Screamer. detest Hairy, detest Dirty and detest Screamer. If detest only Screamer and detest all three, what proportion detest Hairy and Dirty but not Screamer?