Part BCSIR NET December 2024coupled-indices-escape-independent-ones-accumulate

Coupled indices escape independent ones accumulate

Let $N$ be the set of positive integers. Consider $R^{2}$ with the Euclidean topology and the subsets A = { $(n, 1/ n) : n \in N$ } and B = { $(n, 1/ m) : n, m \in N$ }. Which of the following statements is true?

A.A is a closed subset of $R^{2}$ but B is not a closed subset of $R^{2}$ .✓
B.B is a closed subset of $R^{2}$ but A is not a closed subset of $R^{2}$ .
C.Both A and B are closed subsets of $R^{2}$ .
D.Neither A nor B is a closed subset of $R^{2}$ .

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: An arbitrary intersection of open sets is open

Coupled indices escape independent ones accumulate

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