Q.If A = (-7, 3], B = [2, 6] and C = [4, 9] then find B'∩C'.

$B' = \mathbb{R}-[2,6] = (-\infty,2)\cup(6,\infty)$. $C' = \mathbb{R}-[4,9] = (-\infty,4)\cup(9,\infty)$. Now intersect piece by piece: $(-\infty,2)\cap(-\infty,4) = (-\infty,2)$; $(-\infty,2)\cap(9,\infty) = \phi$; $(6,\infty)\cap(-\infty,4) = \phi$; $(6,\infty)\cap(9,\infty) = (9,\infty)$. Collecting the non-empty pieces: $B'\cap C' = (-\infty,2)\cup(9,\infty)$. (This also equals $(B\cup C)'$ by De …

Complement each interval separately (each complement may itself be two pieces), then intersect every piece of one complement against every piece of the other, keeping only …

With two-piece complements on each side, there are up to four pairwise intersections to check — skipping any of the four combinations risk …