IIT Madras MS written test 2019

Question

Which of the following infinite sets have the same cardinality?
$\mathbb{N}$ : Set of Natural numbers

$\mathbb{E}$ : Set of Even numbers

$\mathbb{Q}$ : Set of Rational numbers

$\mathbb{R}$ : Set of Real numbers

 

• A. $\mathbb{N}$ and $\mathbb{E}$
• B. $\mathbb{Q}$ and $\mathbb{R}$
• C. $\mathbb{R}$ and $\mathbb{N}$
• D. None of the above

Comments

only N, E, Q are countably infinite sets.. R is uncountably infinite set.. based on cardinality, sets either have finite size, countably infinite(whose cardinality is denoted by aleph null) and uncountably infinite (whose cardinality is denoted by $\epsilon$)... since first 3 are countably infinite sets, so all these 3 should have same cardinality aleph null.. set of real numbers is uncountably infinite set whose cardinality is more than aleph null..

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yes, u r right.

Subset of natural number is countable.So, Q and R both will be uncountable

https://en.wikipedia.org/wiki/Countable_set

but here asking about infinite set. So, all are infinite. And cardinality of all be different, because all are different in type.

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@ankitgupta.1729

countably infinite set must be a bijective function

right? https://gateoverflow.in/216802/set-theory

Answer 1

it should be D . bcoz every 1 is differ in definition.