 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/discrete-mathematics-continuous-mathematics-and-probability/1/c/solution

Apply the two identities already proved with

A = U

. Every

B_{i}

is a subset of the common universe, and a complement is the set difference from that universe. Therefore

U ∖ ⋃_{i = 1}^{n} B_{i} = ⋂_{i = 1}^{n} (U ∖ B_{i}), U ∖ ⋂_{i = 1}^{n} B_{i} = ⋃_{i = 1}^{n} (U ∖ B_{i}) .

Replacing each set difference from

U

by its complement notation gives the claimed finite forms of De Morgan's laws.

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