This assignment gives us practice with the slightly more tricky process of recognizing necessary and sufficient conditions. For each of the following statements, determine which of the following goes in each blank: (Chapter 3.2) necessary, sufficient, both necessary and sufficient, neither.
1. Having the right key is sufficient for a capable human to be able to open a lock.
2. It having rained recently is sufficient for the ground being wet.
3. Being two hydrogen atoms bonded to an oxygen atom is sufficient for being water.
4. Loving the weather in the winter is neither necessary nor sufficient for being in Tampa.
5. Showing up to class is necessary for getting an A.
6. Being mortal is necessary for being human.
7. Being a rational animal is necessary for being human.
8. Being a featherless biped is neither necessary nor sufficient for being human.
9. Being a mammal is neither necessary nor sufficient for being human.
10. Being a human is sufficient for being a mammal.
11. Being 2, 4, 6, or 8 is sufficient for being an even number.
12. Being 2, 4, 6, or 8 is necessary for being an even number <10.
13. Removing an old diaper is necessary for changing a baby.
14. Having gas in the car is necessary for it to run.
15. Diet and exercise are both necessary and sufficient for living a long time.