Question

Identify the following sets as finite or infinite.

i) $A=$ The set of all straight lines passing through a point.

ii) $B=\{x:x^2-5x+6=0,x\in N\}$

Answer 1

Given,

i) $A=$ The set of all straight lines passing through a point.

As we know through a point there passes an infinite number of lines. So the set $A$ is infinite.

ii) $B=\{x:x^2-5x+6=0,x\in N\}$

Since,

$x^2-5x+6=0$

or, $(x-3)(x-2)=0$

or, $x=2,3$ are natural numbers.

So $B$ contains two elements.

So $B$ is a finite set.