Prove the Bonferroni inequality: For any events E₁, E₂, , Eₙ,
a) P(E₁ ∪ E₂ ∪ ∪ Eₙ) ≥ P(E₁) + P(E₂) + + P(Eₙ)
b) P(E₁ ∩ E₂ ∩ ∩ Eₙ) ≥ P(E₁) ⋅ P(E₂) ⋅ ⋅ P(Eₙ)
c) P(E₁ ∩ E₂ ∩ ∩ Eₙ) ≤ P(E₁) + P(E₂) + + P(Eₙ)
d) P(E₁ ∪ E₂ ∪ ∪ Eₙ) ≤ P(E₁) ⋅ P(E₂) ⋅ ⋅ P(Eₙ)