Question 8: Consider the set \(P=\{x|x=5m,m\in N\}\) and \(Q=\{x|x=2m,m\in N\}\). Find \(P\cap Q\)
Solution:
\(P=\{x|x=5m,m\in N\}\)
\(P=\{5,10,15,…\}\)
\(Q=\{x|x=2m,m\in N\}\)
\(Q=\{2,4,6,…\}\)
\(P\cap Q\)\(\ =\ \)\(\{5,10,15,20,…\}\)\(\cap\)\(\{2,4,6,8,10,…\}\)
\(\ \ \ \ \ \ \ \ \ \ \ = \{10,20,30,40,50…\}\)
Explanation:
\(\text{LCM(2,5)=10}\)
The multiple of \(10\) are \(10,20,30,…\)
To find the intersection of two arithmetic sets (like multiples), always think of the LCM (Least Common Multiple) of their generating numbers. That gives you the set of common elements.