Answer to Question #324661 in Discrete Mathematics for glenn

Question

Let 𝑈 = {𝑎, 𝑒, 𝑖, 𝑜, 𝑢, 3, 6, 9, 12}, 𝐴 = {𝑜, 𝑢, 3, 12}, 𝐵 = {𝑢, 9, 6, 𝑎}, 𝑎𝑛𝑑 𝐶 = {𝑢, 12, 𝑖, 𝑜}.

1. Find 𝐶 ∪ 𝐴

2. Find (𝐶′ ∩ 𝐵) ∪ 𝐶

3. Find {(𝐵′ ∪ 𝐴)′ − 𝐴 ∪ (𝐵 ∩ 𝐵′)}

Answer 1

$1:\\C\cup A=\left\{ o,u,i,3,12 \right\} \\2:\\\left( C'\cap B \right) \cup C=\left( C'\cup C \right) \cap \left( B\cup C \right) =B\cup C=\left\{ u,a,i,o,6,9,12 \right\} \\3:\\\left( B'\cup A \right) '-A\cup \left( B\cap B' \right) =\left[ \begin{array}{c} B\cap B'=F\\ A\cup \left( B\cap B' \right) =A\cup F=A\\\end{array} \right] =\\=\left( B'\cup A \right) '-A=B''\cap A'\cap A'=B\cap A'=B-A=\left\{ a,9,6 \right\} \\\left[ those\,\,of\,\,B\,\,which\,\,are\,\,not\,\,in\,\,A \right]$