Section 1: Problem 6 Solution

Working problems is a crucial part of learning mathematics. No one can learn topology merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.

James R. Munkres

Write the contrapositive of each of the statements of Exercise 5.

The three true contrapositive statements are

(a) $\forall A\in\mathcal{A}:x\notin A\Rightarrow$ $x\notin\cup_{A\in\mathcal{A}}A$ ,

(d) $\exists A\in\mathcal{A}:x\notin A\Rightarrow$ $x\notin\cap_{A\in\mathcal{A}}A$ .

The other one is false,

(b) $\exists A\in\mathcal{A}:x\notin A\Rightarrow$ $x\notin\cup_{A\in\mathcal{A}}A$ .

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Section 1: Problem 6 Solution

Section 1: Problem 6 Solution