Topology

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Cardinality and Relations

TOPO-MKBGKQ

Which of the following sets has the largest cardinality?

A

The set of equivalence relations on $\mathbb{R}$

B

The set of equivalence classes in $\mathbb{R}$ under $\sim$ such that $a\sim b$ iff $a-b\in\mathbb{Q}$

C

$\mathbb{R}\times\mathbb{Q}$

D

The set of irrational numbers.