The Language of Argument

2 1 9

S u f f i c i e n t C o n d i t i o n s a n d N e c e s s a r y C o n d i t i o n s

Indicate whether the following principles are true or false and why.

1. If having feature F is a sufficient condition for having feature G,
   then having feature G is a necessary condition for having feature F.


2. If having feature F is a sufficient condition for having feature G,
   then lacking feature F is a necessary condition for lacking feature G.


3. If lacking feature F is a sufficient condition for having feature G, then
   having feature F is a necessary condition for lacking feature G.


4. If lacking feature F is a sufficient condition for having feature G,
   then lacking feature F is a necessary condition for having feature G.


5. If having either feature F or feature G is a sufficient condition for having
   feature H, then having feature F is a sufficient condition for having feature H.


6. If having either feature F or feature G is a sufficient condition for having
   feature H, then having feature G is a sufficient condition for having feature H.


7. If having either feature F or feature G is a sufficient condition for having
   feature H, then not having feature F is a necessary condition for not having
   feature H.


8. If having both feature F and feature G is a necessary condition for having
   feature H, then lacking feature F is a sufficient condition for lacking feature H.


9. If not having both feature F and feature G is a sufficient condition for having
   feature H, then lacking feature F is a sufficient condition for having feature H.


10. If having either feature F or feature G is a sufficient condition for having
    feature H, then having both feature F and feature G is a sufficient
    condition for having feature H.

Exercise II

10. Not being an integer is a sufficient condition for not being an even number.


11. Being both an integer and divisible by 2 without remainder is a sufficient
    condition for being an even number.


12. Being both an integer and divisible by 2 without remainder is a necessary
    condition for being an even number.


13. Being an integer divisible by 2 without remainder is a necessary condition
    for being an even number.


14. Driving seventy-five miles per hour (for fun) is a sufficient condition for
    violating a legal speed limit of sixty-five miles per hour.


15. Driving seventy-five miles per hour (for fun) is a necessary condition for
    violating a legal speed limit of sixty-five miles per hour.


16. Cutting off Joe’s head is a sufficient condition for killing him.


17. Cutting off Joe’s head is a necessary condition for killing him.


18. Cutting off Joe’s head and then holding his head under water for ten
    minutes is a sufficient condition for killing him.

97364_ch10_ptg01_215-238.indd 219 15/11/13 10:48 AM

some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materiallyCopyright 201^3 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,

affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.