# PHILOSOPHY Natural Deduction NOTE AN ESSAY

Write out the conclusion that follows in a single step from the given premises (please read U as horseshoe):

1.

(S U ∼F) • (∼F U B)

2.

S v ∼F

3.

∼F

QUESTION 2

Write out the conclusion that follows in a single step from the given premises (please read U as horseshoe):

1. ~M U S

2. ~M

3. (M v H) v ~S

QUESTION 3

Write out the conclusion that follows in a single step from the given premises (please read U as horseshoe):

1. (J • ~N) v T

2. ~(J • ~N)

3. J

QUESTION 4

Write out the conclusion that follows in a single step from the given premises (please read U as horseshoe):

1. N v C

2. (N v C) U (F U C)

3. ~C

QUESTION 5

Write out the conclusion that follows in a single step from the given premises (please read U as horseshoe):

1. ~E U P

2. ~P

3. ~(P v ~H)

QUESTION 6

Please complete the following proof using the first eight rules of inference (please read U as horseshoe):

1. M U ~Q

2. (P U ~Q) U (R U ~L)

3. ~L U S

4. P U M                            / R U S

QUESTION 7

Please complete the following proof using the first eight rules of inference (please read U as horseshoe):

1. L v ~S

2. R U (P • ~Q)

3. ~L

4. (P • ~Q) U S              / ~R

QUESTION 8

Please complete the following proof using the first eight rules of inference (please read U as horseshoe):

1. P v (M v R)

2. M U S

3. R U Q

4. ~P                         / S v Q

QUESTION 9

Please complete the following proof using the first eight rules of inference (please read U as horseshoe):

1. (M v N) U (P • K)

2. (P v ~Q) U [(R U L) • S]

3. M                                       / P • (R U L)

QUESTION 10

Please complete the following proof using the first eight rules of inference (please read U as horseshoe):

1. P • ~Q

2. (P v ~R) U (~S • M)

3. (~S • P) U (P U N)             / N

QUESTION 11

Please complete the following proof using the first eight rules of inference (please read U as horseshoe):

1. (P U Q) • (R U S)

2. P v L

3. (L U M) • (N U K)         / Q v M

QUESTION 12

Please complete the following proof using the first eight rules of inference (please read U as horseshoe):

1. P • (S v Q)

2. (P v R) U M          / M

QUESTION 13

Please complete the following proof using the first eight rules of inference (please read U as horseshoe):

1. ~P U Q

2. R • (S U L)

3. (Q • ~M) U (R U ~L)

4. ~P • ~K

5. ~P U ~M                       / ~L

QUESTION 14

Please complete the following proof using the first eight rules of inference (please read U as horseshoe):

1. R U S

2. P U ~Q

3. ~Q U R

4. P • Q                          / R • S

QUESTION 15

Please complete the following proof using the first eight rules of inference (please read U as horseshoe):

1. (Q • R) v ~P

2. R U S

3. [ ~P • ~(Q • R)] U (L U ~Q)

4. ~(Q • R) U (~Q U R)

5. ~(Q • R) • ~M                           / L U S

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