Question

Th e set P = {x | x ∈Z , –1< x < 1} is a
(a) Singleton set
(b) Power set
(c) Null set
(d) Subset

Answer 1

Answer:

The set P = {x | x ∈Z , –1< x < 1} is a

(a) Singleton set

Step-by-step explanation:

The set P = {x | x ∈Z , –1< x < 1} is a  Singleton set

In mathematics, a singleton set , also known as a unit set, is a set with exactly one element

x ∈Z

Z is integer  ..........-3 , -2 , -1 , 0 , 1 , 2, 3 ,,,,,,,,,,,,,

–1< x < 1

=> x = 0

P = { 0 }

Hence P is a Singleton set

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

SINGLETON SET :

A set is said to be a SINGLETON SET if it contains exactly one element

NULL SET :

A set is said to be NULL SET if it contains no element

SET OF INTEGERS

$\sf{A \: set \: of \: integers \: is \: denoted \: by \: \: \mathbb{Z} \: }$

$\sf{ \mathbb{Z} = \{ 0, \pm1, \pm2, \pm3,....... \} }$

TO CHOOSE THE CORRECT OPTION

The set P = {x | x ∈Z , –1< x < 1} is a

(a) Singleton set

(b) Power set

(c) Null set

(d) Subset

CALCULATION

Here the set P is given by

$\sf{P = \{ \: x: x \in \mathbb{Z} \: , \: - 1 < x < 1 \: \: } \}$

Since there is only one integer 0 between - 1 and 1

$\sf{So \: \: P \: = \{ \: 0 \: \}}$

Hence P is a SINGLETON SET

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LEARN MORE FROM BRAINLY

If A and B are two non empty sets then A∪B=B∩A iff *

A⊂B

B⊂A

A=B

None of these

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