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 \(H=\{x:x\text{ is a square}\}\).
\((ii)\) \(\;\) Find \(G \cup H\)
Solution:
\(G=\{1,2,4,8,16,32,64,128\}\)
\(H=\{1,4,9,16,25,36,49,64,81,100,121,144\}\)
\(G \cup H\)=\(G=\{1,2,4,8,16,32,64,128\}\)\(\cup\)\(\{1,4,9,16,25,36,49,64,81,100,121,144\}\)
\(G \cup H\)=\(\{1,2,4,8,9,16,25,32,36,49,64,81,100,121,128,144\}\)
Explanation:
Union \(\cup\) means combine all elements from both sets.
No repetition — each element appears only once, even if it’s in both sets.
Tips for Students:
To find the union, don’t repeat numbers.
Use color-coding or ticks to mark used numbers.