Q.Let $A = \{x : x \in N, x \text{ is a multiple of } 3, x \le 20\}$ and $B = \{x : x \in N, x \text{ is a multiple of } 4, x \le 20\}$. Using a Venn diagram, find $A \cap B$ and describe what this intersection represents.

[!TLDR] Common multiples of 3 and 4 up to 20 are multiples of their LCM, 12. [!ANSWER] $A \cap B = \{12\}$, re …

$A = \{3,6,9,12,15,18\}$ (multiples of 3 up to 20) and $B = \{4,8,12,16,20\}$ (multiples of 4 up to 20). In the Venn diagram, the overlapping region contains numbers that are multiples of both 3 and 4, i.e. multiples of $\mathrm{lcm}(3,4) = 12$. The only such multiple $\le 20$ is 12 itself (t …

List both sets fully, then either scan for shared elements directly or use the LCM shortcu …

A common mistake is including 24 (forgetting the $x \le 20$ bound) or missing that intersection here …