Section 1: Problem 3 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

(a) Write the contrapositive and converse of the following statement: "If $x<0$ , then $x^{2}-x>0$ ," and determine which (if any) of the three statements are true,

(b) Do the same for the statement "If $x>0$ , then $x^{2}-x>0$ ."

Statement	Contrapositive	Converse
$x<0\Rightarrow x^{2}-x>0$ (true)	$x^{2}-x\le0\Rightarrow x\ge0$ (true)	$x^{2}-x>0\Rightarrow x<0$ (false)
$x>0\Rightarrow x^{2}-x>0$ (false)	$x^{2}-x\le0\Rightarrow x\le0$ (false)	$x^{2}-x>0\Rightarrow x>0$ (false)

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Section 1: Problem 3 Solution

Section 1: Problem 3 Solution