Part I: True or False. Are the follow examples a proper application of the rule cited:

1. (A v ~B) ~C
2. ~C
3. ~(A v ~B) Modus Tolens (MT)

1. ~A B
2. ~ B
3. A Modus Ponens (MP)

1. (~C ~D) v (A B)
2. ~C ~D
3. ~(A B) Disjunctive Syllogism (DS)

1. (A v B) ~C
2. A
3. ~C Modus Ponens (MP)

1. (A B) v ~(C v D)
2. ~(A B)
3. C v D Disjunctive Syllogism (DS)

1. A C
2. (A C) B Conjunction (CONJ)

Part II: Cite the rule that used in the following inferences:

1. ~X ~A
2. ~X
3. ~A

1. (X v ~A) B
2. ~B
3. ~(X v ~A)

1. (A B) v ~C
2. ~(A v B)
3. ~C

Part III: Indicate what conclusion will follow from the application of the rule mentioned:

1. (X v Y) ~A
2. (X v Y)
3. MP 1,2

1. (~A B) (A B)
2. ~(A B)
3. MT 1,2

1. (A B) v (X Y)
2. ~(A B)
3. X Y DS 1, 2

Part IV: Construct proofs for the following using any of the rules of inference:

1. (A v B) (C v D) Pr. /
   

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