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**HallsofIvy** Question: does "the complement of B union E" mean "(complement of B) union E" or "complement of (B union E).

If it is the first, then first find the complement of B: Since B= {analysis, topology, calculus} or {0, 1, 1, 0, 0, 0, 1, 0} its complement is {1, 0, 0, 1, 1, 1, 0, 1} (That's a good reason for using that notation- just swap 1s and 0s.)

E= {algebra, calculus, geometry, trigonometry, analysis} or {0, 1, 1, 1, 1, 1, 0, 0} so "(complement of B) union E" is {1, 1, 1, 1, 1, 1, 0, 1}, the "bitwise and" of the two.

But (B union E) is {0, 1, 1, 1, 1, 1, 1, 0} and its complement is {1, 0, 0, 0, 0, 0, 0, 1}.