A very difficult problem There is nothing to do, so try -Out. Strategy Review A very difficult problem 1. -(A>B) A A GOAL There is nothing to do, so try -Out.

Strategy Review A very difficult problem 1. -(A>B) A 2. -A PA ?&-? A 2-? -O -(A>B) is available so use it as part of the contradiction.

Strategy Review A very difficult problem 1. -(A>B) A 2. -A PA (A>B)&-(A>B) 1,? &I A 2-? -O To get this contradiction we will need to prove A>B.

Strategy Review A very difficult problem 1. -(A>B) A 2. -A PA A>B GOAL (A>B)&-(A>B) 1,? &I A 2-? -O Since the GOAL is a conditional, use the >In strategy

A very difficult problem We are stuck. So use the Negation Strategy Strategy Review A very difficult problem 1. -(A>B) A 2. -A PA 3. A PA B GOAL A>B 3-? >I (A>B)&-(A>B) 1,? &I A 2-? -O We are stuck. So use the Negation Strategy

A very difficult problem What is our contradiction? Strategy Review A very difficult problem 1. -(A>B) A 2. -A PA 3. A PA 4. -B PA ?&-? B 4-? -O A>B 3-? >I (A>B)&-(A>B) 1,? &I A 2-? -O What is our contradiction?

A very difficult problem Strategy Review A very difficult problem 1. -(A>B) A 2. -A PA 3. A PA 4. -B PA 5. A&-A 3,2 &I 6. B 4-5 -O 7. A>B 3-6 >I 8. (A>B)&-(A>B) 1,7 &I 9. A 2-8 -O For more click here