Logic: Practice test for Test III.

Note: These problems are typical of those that will be on the exam, though there will likely be a few that are more difficult and a few that are less. You would be well advised that work not only on these, but on all of the starred proofs from the exercises for sections 7.4, 7.5 and 7.6.

Use the 18 rules of inference for doing the following 4 proofs. Do not use conditional or indirect proof.

1)

1. E  (P  B)

2. (E  B)  ~(P  ~M)/ E  M

2)

  1. (L v P)  U
  2. (M  U)  I

3. P/ I

3)[Note: This one is challenging!]

1. D  (B  E)

2. ~H  A

3. (A  C)  ~G

4. A  D

5. (B  C)  ~H/ A  (B  C)

4)

1. S  (D  I)

2. S v (U  D)/ D

5)

1. ~(A v ~D)

2. ~A  (B v C)

3. ~C v ~D

4. (B v E)  [F  (G  ~D)]/ ~(F  G)

Use the conditional method for the following 2 proofs.

6)

1. P  (I  W)

2. I  (W  ~S)/ P  (I  ~S)

7)

1. A  H

2. (F v W)  L/ (H  F)  (A  L)

For the following two proofs, use the indirect method.

8)

1. R  B

2. R  (B  F)

3. B  (F  H)/ R  H

9)

1. (Z  C)  B

2. (V  Z)  B/ B

Note: Be sure you understand the strategies for #19 from section 7.6!