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Let $\text{A, B}$ be two non-empty sets, with cardinality $3,4$ respectively. Let $\text{R}$ be a relation defined on the power set of $\text{A} \times \text{B}.$ Relation $\text{R}$ is reflexive, symmetric, transitive and antisymmetric.

How many equivalence classes does relation $\text{R}$ have?
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| A | = 3 and | B | = 4, thus | AxB | = 12. 

| P(AxB) | = 2^12.

Relation R : P(AxB) → P(AxB).

R is reflexive, symmetric, transitive and anti-symmetric. This is only possible if R is identity relation.

Therefore, # equivalence classes = | R | = | P(AxB) | = 2^12 = 4096.

(In this case, every element will have its own unique equivalence class. )

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