If $A = \{x: x = 4n, n ∈ Z\}$ and $B=\{x: x = 6n, n∈ Z\}$, then $A∩B =$

$\{x: x = 2n, n∈ Z\}$ $\{x: x = 10n, n∈ Z\}$ $\{x: x = 12n, n∈ Z\}$ $\{x: x = 24n, n∈ Z\}$

$\{x: x = 12n, n∈ Z\}$

The correct answer is Option (3) → $\{x: x = 12n, n∈ Z\}$ We have, $x∈A∩B$ $⇒ x = 4n$ and $x = 6n, n ∈ Z$ ⇒ $x$ is a multiple of 4 and $x$ is a multiple of 6 ⇒ $x$ is a multiple of 4 and 6 both ⇒ $x$ is a multiple of 12 $⇒ x = 12n, n∈ Z$ Hence, $A∩B = \{x: x = 12n, n ∈ Z\}$