Question 2: Let, \(U=\{x:x\text{ is an integer and }0<x\leq150\}\), \(G=\{x:x=2^m\text{ for integer m and }0\leq m\leq 12 \}\) and \(H=\{x:x\text{ is a square}\}\).
\((iii)\) \(\;\) Find \(G \cap H\)
Solution:
\(G=\{1,2,4,8,16,32,64,128\}\)
\(H=\{1,4,9,16,25,36,49,64,81,100,121,144\}\)
\(G \cap H\)=\(G=\{1,2,4,8,16,32,64,128\}\)\(\cap\)\(\{1,4,9,16,25,36,49,64,81,100,121,144\}\)
\(G \cap H\)=\(\{1,4,16,64\}\)
Explanation:
Intersection \(\cap\) means the common elements in both sets.
Tips for Students:
- Use a highlighter or circle common elements in both lists.
- Always write sets in increasing order for easier comparison.