CRITICAL THINKING

Fill in the blanks to complete the following proof.

Some of the blanks may be conclusions. In that case place one of our ASCII-alternate propositional logic symbols (some of which are more than one keyboard stroke) in each blank, and do not add any space before, after, or between your keyboard strokes. Use the following symbols.

tilde: ~

dot: . (that's a period)

wedge: v (that's a lowercase vee "v")

horseshoe: -> (that's a dash followed by a right corner bracket)

triple bar: <-> (that's a left corner bracket, followed by a dash, followed by a right corner bracket

In other cases, the blank is a rule. Fill in the blank with the full name of the rule or the abbreviation from the book. Other abbreviations will be marked wrong.

1. A -> (B -> ~ C)

2. D -> (A . C)

3. A -> (~~ C -> ~B) 1,_________________

4. A -> (C -> ~ B) 3,___________________

5. (A . C) -> ~B 4, ___________________

6. __________ __________ ____________ __________ 2,5, HS

Complete the proof with the given assumptions, using any combination of the 18 rules of inference.

1. (A v D) -> (B v C)

2. A

3. ~ B /prove C

Complete the proof with the given assumptions, using any combination of the 18 rules of inference.

1. (A -> (B -> C)) . (~B -> D)

2. (A . B) v ~ B

3. ~ C /prove D