Question

2. Which of the following is a null set ?
O { x:Ix! = 5 , x€N)
O {x: 2x+1<2, x€Z }
Ο Ο Ο Ο
{x:\xl <1 , x€N)
none of these​

Answer 1

Answer:

none if this ans diiikkkkkkkkkk

Answer 2

$\bf \huge\color{pink}{Hola!}$

AnsweR :

$\sf \mapsto option \: \: a$

SolutioN :

For,

$\sf S_1 = \{ \: x : \: x! = 5 \: \: ; \: \: x \in \: N \}$

$\mapsto \sf d_{s_{1}}= \phi$

Hence, it's null set

_____________

Checking for anothers,

$\sf S_2 = \{ \: x : \: 2x + 1 < 2 \: \: ; \: \: x \in \: Z\}$

$\mapsto \sf d_{s_{2}}$

$\implies \: \sf \: 2x + 1 < 2$

$\implies \: \sf \: x < \frac{1}{2}$

$\implies \sf \: x \in \: ( - \infty ,\frac{1}{2} )$

→ Having elements in domain

$\mapsto \sf \:hence \: \: its \: \: not \: \: a \: \: null \: \: set$

_____________

$\sf S_2 = \{ \: x : \: |x| < 1\: \: ; \: \: x \in \: N\}$

$\mapsto \sf d_{s_{3}}$

$\implies \sf \: x \in \: (0,1)$

→ Having elements in domain

$\mapsto \sf \:hence \: \: its \: \: not \: \: a \: \: null \: \: set$

______________

HOPE THIS IS HELPFUL...