Necessary and sufficient conditions                       Instructor: Oscar Clemotte

 

Necessary conditions are like minimun requirements.

A is a necessary condition of B if and only if B cannot occur without the occurrence of A.

 

Or

 

A is a necessary condition of B if B could not be the case without A being the case.

 

Example: Oxygen is a necessary condition for fire, but not sufficient.

 

In other words

 

This (Oxygen) is a necessary condition for that (fire) if and only if that (fire) cannot be without this (Oxygen). A necessary condition for the occurrence of a specified event (fire) is a circumstance (Oxygen) in whose absence the event cannot occur.

 

Sufficient conditions, instead, are enough to bring about a particular event or property.

 

A is a sufficient condition of B if and only if whenever A occurs, B also occurs.

 

Or

 

A is a sufficient condition of B if A could not be the case without B's being the case.

 

Example: Sugar is a SUFFICIENT condition for sweetness.

 

In other words

 

This (Sugar) is a sufficient condition for that (sweetness) if and only if this (Sugar) alone guarantees that (sweetness).

 

A sufficient condition for the occurrence of a specified event (sweetness) is a circumstance in whose presence (Sugar) the event (sweetness) will occur.

 

 

Exercises

Directions:  Label the relationship between the given examples as either:

(1)  Necessary (but NOT sufficient),

(2)  Sufficient (but NOT necessary),

(3)  Neither necessary nor sufficient.  

 

1.  Fire is a ______________ condition for oxygen.  

2.  Striking a match is a ______________ condition for lighting a match.  

3.  Sweetness is a _______________ condition for sugar.

4.  Five nickels is a ___________ condition for twenty-five cents.  

5.  Blackness is a _____________ condition for being a raven.  

6.  Being at least 15 years of age is a _____________  condition for being 25 years of age.

7.  Mortality is a _____________ condition for being a human.  

8.  Yellowness is a ________________ condition for being a banana.  

9. A banana is a _____________ condition for yellowness.

10.  Being a flower is a _______________ condition for being a rose.  

11. Being a bachelor is a _______________ condition for an unmarried adult male.

 


 

ANSWERS

1.  Fire is a ______________ condition for oxygen.  SUFFICIENT

2.  Striking a match is a ______________ condition for lighting a match.  NEITHER NECESSARY NOR SUFFICIENT (it might not light, or you could light the match with a lighter)

3.  Sweetness is a _______________ condition for sugar.  NECESSARY (if it is granulated, not cane sugar)

4.  5 nickels is a ___________ condition for twenty-five cents.  SUFFICIENT

5.  Blackness is a _____________ condition for being a raven.  NECESSARY

6.  Being at least 15 years of age is a _____________  condition for being 25 years of age. NECESSARY

7.  Mortality is a _____________ condition for being a human.  NECESSARY (all humans are mortal)

8.  Yellowness is a ________________ condition for being a banana.  NEITHER NECESSARY OR SUFFICIENT (the banana might be black)

9. A banana is a _____________ condition for yellowness. NEITHER NECESSARY OR SUFFICIENT (the banana might be black)

10.  Being a flower is a _______________ condition for being a rose.  NECESSARY

11. Being a bachelor is a _______________ condition for an unmarried adult male. BOTH (??)