Question:medium
Let
\[
S=\{1,2,3,\ldots,10\}.
\]
Consider the set
\[
X=\{R : R \text{ is an equivalence relation on } S \text{ such that } R \text{ has exactly } 42 \text{ elements}\}.
\]
Then the number of elements in \(X\) is __________.
Let
\[
S=\{1,2,3,\ldots,10\}.
\]
Consider the set
\[
X=\{R : R \text{ is an equivalence relation on } S \text{ such that } R \text{ has exactly } 42 \text{ elements}\}.
\]
Then the number of elements in \(X\) is __________.
Show Hint
If equivalence classes have sizes:
\[
n_1,n_2,\ldots,n_k
\]
then total elements in the relation are:
\[
n_1^2+n_2^2+\cdots+n_k^2
\]
Updated On: May 20, 2026
Show Solution
Correct Answer: 1260
Solution and Explanation
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