If A = x: x = 4n, n ∈ Z and B=x: x = 6n, n∈ Z, then A∩B =

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, $A∩B = \{x: x = 12n, n ∈ Z\}$