Test #4 Study Guide

Test #4 Study Guide

I.By using any of the rules of implication and replacement, select the conclusion that follows in a single step from the given premises. There is only one correct answer. There will be 25 questions on the test, each worth 4 points. There will be 3 proofs as well for extra credit (each will be worth up to 15 points).

1.1.R R

2.N • T

3.R (N • T)

a.T2, Simp

b.(N • T) R3, Trans

c.R2, 3, MT

d.R  (N T)3, DM

e.R1, Taut

2.1.G • A

2.K  (G • A)

3.G  M

a.(K G )A2, Exp

b.K  (A • G)2, Com

c.(K  G) • A2, Assoc

d.K1, 2, MP

e.M1, 3, MP

3.1.(Q • S)

2.F  (Q • S)

3.H  (Q • S)

a.(H • Q)  (H • S)3, Dist

b.Q  S1, DM

c.F1, 2, MT

d.H1, 3, DS

e.F1, 2, MT

4.1.N

2.R N

3.C • (T  R)

a.C3, Simp

b.T N2, 3, HS

c.(C • T)  R3, Assoc

d.R1, 2, MT

e.N R2, Trans

5.1.(K • T)  (K • H)

2.M  (K • H)

3.(K • H)

a.K  H3, DM

b.K • T1, 3, DS

c.K • (T H)1, Dist

d.M2, 3, MT

e.(M • K) H2, Exp

6.1.A

2.G  (A L)

3.A G

a.A  G3, DN

b.(G  A) L2, Assoc

c.L1, 2, MP

d.G1, 3, DS

e.G  (L A)2, Trans

7.1.(S F) • (F  B)

2.S F

3.F

a.S  B1, HS

b.F  B1, 2, CD

c.S2, 3, DS

d.B1, 3, MP

e.S1, 3, MT

8.1.N  R

2.(N • R)  C

3.N

a.(N  R)  (R  N)1, Equiv

b.N • (R  C)2, Assoc

c.C  (N • R)2, Com

d.N  (R  C)2, Exp

e.R1, 3, MP

9. 1.M  S

2. M

3. (M  H) S

a.H2, 3, DS

b.M  H3, Simp

c.M  (H S)3, Assoc

d.S1, 2, MP

e.M  S1, Impl

10.1.(J • N)  T

2.(J • N)

3.T

a.T1, 2, DS

b.J  N2, DM

c.J • N1, 3, DS

d.J • (N  T)1, Assoc

e.J2, Simp

11.1.U  (S • K)

2.R  (U • U)

3.S U

a.(U • S)  K1, Exp

b.R  U2, DN

c.R U2, Taut

d.R  (S • K)1, 2, HS

e.(S  U) • (U S)3, Equiv

12.1.I B

2.M I

3.I

a.M B1, 2, HS

b.B1, 3, DS

c.M2, 3, MT

d.I  M2, Com

e.(I • B)1, DM

13.1.N • F

2.K  (N • F)

3.U  (K • N)

a.K1, 2, MT

b.(U  K) • N3, Assoc

c.(K • N)  F2, Exp

d.(U  K) • (U N)3, Dist

e.(N • F)1, DM

14.1.D  H

2.D

3.(D  S)

a.H1, 2, MT

b.D  (D  H)2, Add

c.H  D1, Com

d.S2, 3, DS

e.D S3, DM

15.1.A

2.(A T) G

3.Q  (A T)

a.Q  (T A)3, Trans

b.(Q  A) T3, Assoc

c.A  (T • G)2, Exp

d.T1, 3, MP

e.Q G2, 3, HS

16.1.P • (H  D)

2.(P • H)

3.(P H) • (P  H)

a.P H3, Equiv

b.H  D1, Simp

c.(P • H)  D1, Assoc

d.P • (H  D)1, Impl

e.P • H2, DN

17.1.N  C

2.(N  C)  (F  C)

3.C

a.F  C1, 2, MP

b.N1, 3, DS

c.F2, 3, MT

d.N1, 3, MT

e.C • R3, Add

18.1.(S • J)  (S • J)

2.S S

3.J  P

a.S2, Taut

b.J J1, 2, CD

c.S J1, Equiv

d.J  P3, Impl

e.P  J3, Trans

19.1.Q  (A T)

2.T

3.A T

a.Q  (A T)1, DN

b.(A T)  Q1, Com

c.(Q  A) T1, Assoc

d.Q1, 3, MP

e.A2, 3, DS

20.1.E  P

2.P

3.(P H)

a.H2, 3, DS

b.P • (P H)2, 3, Conj

c.P • H3, DM

d.E1, 2, MT

e.P  E1, Trans

21.1.P

2.L  (P  M)

3.(P • M)  (R R)

a.(P • M) R3, Taut

b.P3, Simp

c.L  (R R)2, 3, HS

d.(L  P)  (L  M)2, Dist

e.M1, 2, DS

22.1.N  H

2.Q (N  H)

3.(N  Q) • (H  Q)

a.Q  (N • H)2, DM

b.H  Q3, Simp

c.Q1, 2, MT

d.N (N  H)2, 3, HS

e.Q Q1, 3, CD

23.1.R  (E • D)

2.R • G

3.E  G

a.G2, Simp

b.E • D1, 2, MP

c.E2, 3, MT

d.(R • G)  F2, Add

e.E  G3, Impl

24.1.(L  M) • (F  J)

2.M (F  L)

3.F  L

a.L (F  L)1, 2, HS

b.M  J1, 3, CD

c.L  M1, Simp

d.M2, 3, MT

e.M  (F L)2, DM