Proofs

Practice with Inference Rules

Fill in the blanks, and click "Submit" to see if your answer is correct. Sometimes the blank is a conclusion; sometimes it's a premise. Sometimes it's the name of a rule. Use the standard abbreviation if it's the name of a rule. To get it right, you have to type your answer in just the right format. Use capital letters, not lowercase. Exclude parentheses that would surround the entire sentence. Put a space between a binary operator and the sentences it connects. Put a space between a tilde and any sentence on its right, even one that also starts with a tilde. Don't add any spaces before or after the entire sentence. Use the following symbols in place of those your keyboard doesn't have:

For dot, use a regular period.
For wedge, use a lowercase v.
For horseshoe, use "->". (That's a dash followed by a right corner bracket.)
For triple bar, use "<->". (That's a left corner bracket, a dash, and then a right corner bracket.

1. A v B
2. ~ A
3. 1,2, DS
1. A v (B . C)
2. ~ A
3. 1,2, DS
1. (A . B) v (B -> C)
2. ~ (A . B)
3. 1,2, DS
1. [(A -> B) . (D v ~ E)] v [(A -> B) . (~ D . E)]
3. (A -> B) . (~ D . E) 1,2, DS
1. A -> B
2. A
3. 1,2, MP

1. A -> (B . C)
2. A
3. 1,2, MP
1. (A . B) -> C
2. (A . B)
3. 1,2, MP
1. A -> (B . C)
2. ~ (B . C)
3. 1,2, MT
1. (A -> B) . (C -> D)
2. A v C
3. 1,2, CD
1. [(A . B) -> C] . [D -> (E . F)]
2. (A . B) v D
3. 1,2, CD

Introduction to Logic

Practice with Inference Rules