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We need to give a example of subset of $$R^{2}$$ that is neither closed nor bounded.

Here, we have to find the example of subsets belonging to $$R^{2}$$.

By definition, $$R^{2}=\{(x,y)\mid x,y \epsilon R \}$$

An example of subset of $$R^{2}$$ that is neither closed nor bounded can be given as, $$\{(x,y)\mid x>0\}$$

We need to give a example of subset of $$R^{2}$$ that is closed but not bounded.

An example of subset of $$R^{2}$$ that is closed but not bounded can be given as, $$\{(x,y)\mid x\geq 0\}$$

We need to give a example of subset of $$R^{2}$$ that is not closed but bounded.

An example of subset of $$R^{2}$$ that is not closed but is bounded can be given as, $$\{(x,y)\mid x^{2}+y^{2}<1\}$$

We need to give a example of subset of $$R^{2}$$ that is closed and bounded.

An example of subset of $$R^{2}$$ that is closed and bounded can be given as, $$\{(x,y)\mid x^{2}+y^{2}\leq 1\}$$