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Logic HW!!

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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