Answer to Question #101186 in Discrete Mathematics for LUDNOR

Question #101186

given 2 sets A and B, use membership table to show that (A-B)∪(B-A)=(A∪B) -(A∩B)

Expert's answer

"\\def\\arraystretch{1.5}\n \\begin{array}{c:c:c:c:c}\n A & B & A-B & B-A & (A-B\\cup (B-A) \\\\ \\hline\n 1 & 1 & 0 & 0 & 0 \\\\ \\hline\n 1 & 0 & 1 & 0 & 1\\\\ \\hline\n 0 & 1 & 0 & 1 & 1\\\\ \\hline\n 0 & 0 & 0 & 0 & 0\n\\end{array}"

"\\def\\arraystretch{1.5}\n \\begin{array}{c:c:c}\n A\\cup B & A\\cap B & (A\\cup B)-(A\\cap B) \\\\ \\hline\n 1 & 1 & 0 \\\\ \\hline\n 1 & 0 & 1 \\\\ \\hline\n 1 & 0 & 1 \\\\ \\hline\n 0 & 0 & 0 \n\\end{array}"

Hence

"(A-B)\\cup(B-A)=(A\\cup B)-(A\\cap B)"