Numbers and Sets | Part IA, 2001

State and prove the principle of inclusion-exclusion. Use it to calculate ϕ(4199)\phi(4199), where ϕ\phi is Euler's ϕ\phi-function.

In a certain large college, a survey revealed that 90%90 \% of the fellows detest at least one of the pop stars Hairy, Dirty and Screamer. 45%45 \% detest Hairy, 28%28 \% detest Dirty and 46%46 \% detest Screamer. If 27%27 \% detest only Screamer and 6%6 \% detest all three, what proportion detest Hairy and Dirty but not Screamer?

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