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Chapter 6: Q11. (page 210)
Express the following statement in if-then form.
All marathoners have stamina.
The if-then form of 鈥淎ll marathoners have the stamina鈥� is 鈥淚f a person is a marathoner, then the person has stamina鈥�.
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For the following conditional statement, classify the statement as true or false.
If then .
Classify the following conditional as true or false.
If , then .
Arrange sentences (a)-(e) in an order that completes an indirect proof of the following statement: In a plane, two lines perpendicular to a third line are parallel to each other.
Given: Lines a, b and t lie in a plane;
Prove:
(a) Then a intersects b in some point Z.
(b) But this contradicts the theorem which says that there is exactly one line perpendicular to a given line through a point outside the line.
(c) It is false that a is not parallel to b, and it follows that
(d) Assume temporarily that a is not parallel to b.
(e) Then there are two lines through Z and perpendicular to t.
Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.
If is not a multiple of 3, then n is not a multiple of 3.
Prove that if two lines are perpendicular to the same plane, then the lines do not intersect.
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