Translating Necessary and Sufficient Conditions
Answers 1-6.

 

 

Translate the following English sentences into Propositional  Logic. Use ">" for the horseshoe and "iff" for the triplebar.  Provide a dictionary, separating dictionary entries with a semi-colon.

1.A necessary condition for the death of a vampire is a wood stake through the heart.
 

dictionary: A: A vampire dies.

B: A wood stake goes through a vampire's heart.
translation: A > B


 

2 A sufficient condition for a flood is the presence of water over the high water mark.
 

dictionary: A: There is a flood.

B: Water is over the high water mark.
translation: B > A

 

3 A necessary condition for being human is having a heart.
 

dictionary: A: Something is human.

B: Something has a heart.
translation: A > B

 

4. Having a kidney is not a necessary condition for being a water bug.
 

dictionary: A: Something has a kidney.

B: Something is a water bug.
translation: ~(B > A)

 

5. A sufficient condition for being human is being a featherless biped.

 

dictionary: A: Something is human.

B: Something is featherless.

C: Something is a biped
translation: (B & C) > A

 

6. Rationality is not a necessary condition for caninehood.
 

dictionary: A: Something is rational.

B: Something is a canine.
translation: ~(B > A)