Find (A − C) × (B − C) for A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}
Question
If
\[ A=\{1,2,4\},\ B=\{2,4,5\}\ \text{and}\ C=\{2,5\}, \]
write
\[ (A-C)\times(B-C) \]
Solution
\[ A-C=\{1,4\} \]
\[ B-C=\{4\} \]
Therefore,
\[ (A-C)\times(B-C)=\{1,4\}\times\{4\} \]
\[ =\{(1,4),(4,4)\} \]
Hence,
\[ \boxed{\{(1,4),(4,4)\}} \]