Let \(U=\{1,2,3,\ldots,40\}\), \(A=\{x:x\text{ is divisible by }4\}\), and \(B=\{x:x\text{ is divisible by }5\}\). What is \(n(A\cup B)\)?

16

There are \(\lfloor40/4\rfloor=10\) multiples of 4 and \(\lfloor40/5\rfloor=8\) multiples of 5. Numbers counted in both sets are multiples of \(\operatorname{LCM}(4,5)=20\), namely 20 and 40, so there are 2 common elements. By inclusion-exclusion, \(n(A\cup B)=10+8-2=16\). Therefore, option B is correct.

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).