Question 14: A shopping mall has 100 products from various categories labeled 1 to 100, representing the universal set \(U\). The product are categorized as follows:
\(\quad\bullet\quad\) Set \(A\): Electronics, consisting of 30 prodcts labeled from 1 to 30.
\(\quad\bullet\quad\) Set \(B\): Clothing comprises 25 products labeled from 31 to 55.
\(\quad\bullet\quad\) Set \(C\): Beauty Products, comprising 25 products labeled from 76 to 100.
Write each set in tabular form, and find the union of all three sets.
Solution:
\(U=\{1,2,3,\ldots,100\}\)
\(A=\{1,2,3,\ldots,30\}\)
\(B=\{31,32,33,\ldots,55\}\)
\(C=\{76,77,78,\ldots,100\}\)
\(A\cup B \cup C\)\(\ =\ \)\(\{1,2,3,\ldots,30\}\)\(\cup\)\(\{31,32,33,\ldots,55\}\)\(\cup\)\(\{76,77,78,\ldots,100\}\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(\ =\ \)\(\{1,2,3,\ldots,55,76,77,78,\ldots,100\}\)