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Chapter 6: Q12. (page 210)

Express each statement in if-then form.

Suppose 鈥淎ll marathoners have stamina鈥� is a true conditional. What, if anything, can you conclude from each additional statement? If no conclusion is possible say no.

  1. Nick is a marathoner.
  2. Heidi has stamina.
  3. Mimi does not have stamina.
  4. Arlo is not a marathoner.

Short Answer

Expert verified

a. Nick has stamina.

b. Heidi can be a marathoner or not.

c. Mimi is not a marathoner.

d. Arlo can have stamina or not.

Step by step solution

01

a.Step 1- Consider the statements.

True condition: 鈥淎ll marathoners have stamina鈥�

Additional statement: Nick is a marathoner.

02

Step 2- Step description.

It can be concluded from the additional statement that Nick has stamina because he is a marathoner and all marathoners have stamina.

03

Step 3- Step description.

Therefore, Nick has stamina.

04

b.Step 1- Consider the statements.

True condition: 鈥淎ll marathoners have stamina鈥�

Additional statement: Heidi has stamina.

05

Step 2- Step description.

It can be concluded from the additional statement that it is not compulsory that Heidi is a marathoner. She can be a marathoner or not.

06

Step 3- Step description.

Therefore, Heidi can be a marathoner or not.

07

c.Step 1- Consider the statements.

True condition: 鈥淎ll marathoners have stamina鈥�

Additional statement: Mimi does not have stamina.

08

Step 2- Step description.

It can be concluded from the additional statement that Mimi is not a marathoner. She does not have stamina which is a true condition for being a marathoner.

09

Step 3- Step description.

Therefore, Mimi is not a marathoner.

10

d.Step 1- Consider the statements.

True condition: 鈥淎ll marathoners have stamina鈥�

Additional statement: Arlo is not a marathoner.

11

Step 2- Step description.

It can be concluded from the additional statement that Arlo can have stamina or cannot have stamina.

12

Step 3- Step description.

Therefore, Arlo can have stamina or not.

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For the following figure, name the largest and the smallest angle of the triangle.

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