Theoretical Computer Science Symbolic and Mathematical Logic Questions

  

Its a bunch of problems but each of them are “Select the conclusion that follows in a single step from the given premises in each problem. I did the best to format it quickly in the attached document sorry if I could just take a few pictures. They are multiple choice though,

Instructions
INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises in
each problem.
Question 1
Given the following premises:
1. R  R
2. N • T
3. R  (N • T)
Group of answer choices
R  (N  T) —— ( 3, DM)
R —— ( 2, 3, MT)
(N • T)  R —— ( 3, Trans)
R —— (1, Taut)
T —— (2, Simp)
Question 2
Given the following premises:
1. G • A
2. K  (G • A)
3. G  M
Group of answer choices
K —— (1, 2, MP)
K  (A • G) —— (2, Com)
M —— (1, 3, MP)
(K  G) • A —— (2, Assoc)
(K  G )  A —— (2, Exp)
Question 3
Given the following premises:
1. (Q • S)
2. F  (Q • S)
3. H  (Q • S)
Group of answer choices
H ———- (1, 3, DS)
Q  S ——– ( 1, DM)
F ——— (1, 2, MT)
(H • Q)  (H • S) —— ( 3, Dist)
F ——– (1, 2, MT)
Question 4
Given the following premises:
1.
N
2.
R ⊃ ~N
3.
~C · (T ⊃ R)
Group of answer choices
R ——– (1, 2, MT)
(C • T)  R ——— ( 3, Assoc)
N  R ——— ( 2, Trans)
T  N ——– (2, 3, HS)
C ———- ( 3, Simp)
Question 5
Given the following premises:
1.
(K · ~T)  (K · ~H)
2.
~M ⊃ (K · ~H)
3.
~(K · ~H)
Group of answer choices
K  H ———– (3, DM)
K • T ———– ( 1, 3, DS)
M ——– ( 2, 3, MT)
(M • K)  H —— (2, Exp)
K • (T  H) ——- (1, Dist)
Question 6
Given the following premises:
1.
A
2.
G ⊃ (A ⊃ ~L)
3.
~A  ~G
Group of answer choices
G  (L  A) ——–(2, Trans)
G ——— ( 1, 3, DS)
L ———– ( 1, 2, MP)
(G  A)  L ———– (2, Assoc)
A  G ———– ( 3, DN)
Question 7
Given the following premises:
1.
(S ⊃ ~F) · (~F ⊃ B)
2.
S  ~F
3.
~F
Group of answer choices
F  B ——— (1, 2, CD)
S ——— ( 2, 3, DS)
S ———– (1, 3, MT)
B ———— (1, 3, MP)
S  B ———- (1, HS)
Question 8
Given the following premises:
1.
N ≡ R
2.
(N · ~R) ⊃ C
3.
N
Group of answer choices
R ——- (1, 3, MP)
N • (R  C) ——- ( 2, Assoc)
(N  R)  (R  N) ——- (1, Equiv)
C  (N • R) ——- ( 2, Com)
N  (R  C) ——- (2, Exp)
Question 9
Given the following premises:
1.
~M ⊃ S
2.
~M
3.
(M  H)  ~S
Group of answer choices
M  (H  S) ——- 3, Assoc
M  H ——- 3, Simp
S ——- 1, 2, MP
H ——- 2, 3, DS
M  S ——- 1, Impl
Question 10
Given the following premises:
1.
(J · ~N)  T
2.
~(J · ~N)
3.
~T
Group of answer choices
T ——- 1, 2, DS
J ——- 2, Simp
J  N ——- 2, DM
J • (N  T) ——- 1, Assoc
J • N ——- 1, 3, DS
Question 11
Given the following premises:
1.
~U ⊃ (S · K)
2.
R ⊃ (~U · ~U)
3.
S ≡ ~U
Group of answer choices
(S  U) • (U  S) ——- 3, Equiv
R  U ——- 2, DN
R  (S • K) ——- 1, 2, HS
R  U ——- 2, Taut
(U • S)  K ——- 1, Exp
Question 12
Given the following premises:
1.
~I  ~~B
2.
M ⊃ ~I
3.
I
Group of answer choices
I  M ——- 2, Com
M ——- 2, 3, MT
B ——- 1, 3, DS
(I • B) ——- 1, DM
M  B ——- 1, 2, HS
Question 13
Given the following premises:
1.
~N · ~F
2.
K ⊃ (N · F)
3.
U  (K · ~N)
Group of answer choices
(U  K) • N ——- 3, Assoc
(N • F) ——- 1, DM
K ——- 1, 2, MT
(U  K) • (U  N) ——- 3, Dist
(K • N)  F ——- 2, Exp
Question 14
Given the following premises:
1.
D⊃ H
2.
~D
3.
~(D  S)
Group of answer choices
D  S ——- 3, DM
H ——- 1, 2, MT
S ——- 2, 3, DS
D  (D  H) ——- 2, Add
H  D ——- 1, Com
Question 15
Given the following premises:
1.
A
2.
(A ⊃ ~T) ⊃ ~G
3.
Q ⊃ (A ⊃ ~T)
Group of answer choices
Q  (T  A) ——- 3, Trans
T ——- 1, 3, MP
(Q  A)  T ——- 3, Assoc
A  (T • G) ——- 2, Exp
Q  G ——- 2, 3, HS
Question 16
Given the following premises:
1.
P · (~H  D)
2.
~(~P · ~H)
3.
(P ⊃ ~H) · (~P ⊃ H)
Group of answer choices
(P • H)  D ——- 1, Assoc
P • (H  D) ——- 1, Impl
H  D ——- 1, Simp
P  H ——- 3, Equiv
P • H ——- 2, DN
Question 17
Given the following premises:
1.
N C
2.
(N  C) ⊃ (F ⊃ C)
3.
~C
Group of answer choices
N ——- 1, 3, MT
F  C ——- 1, 2, MP
F ——- 2, 3, MT
N ——- 1, 3, DS
C • R ——- 3, Add
Question 18
Given the following premises:
1.
(S · ~J)  (~S · ~~J)
2.
S  ~S
3.
~J ⊃ P
Group of answer choices
P  J ——- 3, Trans
J  P ——- 3, Impl
S  J ——- 1, Equiv
J  J ——- 1, 2, CD
S ——- 2, Taut
Question 19
Given the following premises:
1.
Q ⊃ (A  ~T)
2.
T
3.
A  ~T
Group of answer choices
Q ——- 1, 3, MP
Q  (A  T) ——- 1, DN
A ——- 2, 3, DS
(Q  A)  T ——- 1, Assoc
(A  T)  Q ——- 1, Com
Question 20
Given the following premises:
1.
~E ⊃ P
2.
~P
3.
~(P  ~H)
Group of answer choices
H ——- 2, 3, DS
P • (P  H) ——- 2, 3, Conj
P  E ——- 1, Trans
E ——- 1, 2, MT
P • H ——- 3, DM
Question 21
Given the following premises:
1. N
2. K  N
3. N  (K • S)
Group of answer choices
(N  K) • S 3, Assoc
K 1, 2, MT
(N • K)  (N • S) 3, Dist
K • S 1, 3, DS
N  K 2, Trans
Question 22
Given the following premises:
1. Q  (H • F)
2. (Q • M)
3. G  (Q • M)
Group of answer choices
Q  (H  F) 1, DM
G  (Q • M) 2, Add
G 2, 3, MT
Q  M 2, DM
Q 2, Simp
Question 23
Given the following premises:
1. (S  R)  (J  T)
2. (P  R)  (S  R)
3. R  J
Group of answer choices
P  J 2, 3, HS
R  T 1, 3, HS
(P  R)  (J  T) 1, 2, HS
S  J 1, 3, HS
(S  R) • (P  R) 1, 2, Conj
Question 24
Given the following premises:
1. Q  (H • L)
2. H  Q
3. L  Q
Group of answer choices
Q  Q 1, 3, HS
H  L 2, 3, HS
(Q  H)  L 1, Exp
(L  Q) • (H  Q) 2, 3, Conj
L  (H • L) 1, 3, HS
Question 25
Given the following premises:
1. F  J
2. A  (F • J)
3. A • (Q  N)
Group of answer choices
(A  F) • (A  J) 2, Dist
A • (N  Q) 3, Com
(A • Q)  N 3, Assoc
A  J 1, 2, HS
J  F 1, Com
Question 26
Given the following premises:
1. D  T
2. D  (T • R)
3. D
Group of answer choices
(D  T) • (D  R) 2, Dist
T • R 2, 3, DS
(D  T) • R 2, Assoc
T 1, 3, DS
D  T 1, DN
Question 27
Given the following premises:
1. (C • F)  E
2. G  (C • F)
3. (C • F)
Group of answer choices
G  E 1, 2, HS
G 2, 3, DS
C  (F  E) 1, Exp
(G  C) • F 2, Assoc
C 1, Simp
Question 28
Given the following premises:
1. K  H
2. (K  H)  (B  J)
3. J  D
Group of answer choices
K 1, Simp
D  J 3, Trans
B  D 2, 3, HS
B  J 1, 2, MP
H  K 1, Impl
Question 29
Given the following premises:
1. R • S
2. R  (S • F)
3. S  (F • N)
Group of answer choices
F • N 1, 3, MP
R  (S  F) 2, DM
(S  F) • (S  N) 3, Dist
S 1, Simp
(S • F)  N 3, Exp
Question 30
Given the following premises:
1. T  E
2. K  (T  T)
3. M  (K  L)
Group of answer choices
K  E 1, 2, HS
M  (K  L) 3, Impl
(M  K)  L 3, Assoc
K  T 2, Taut
M  (K  L) 3, DN
Question 31
Given the following premises:
1. R  R
2. R  (J • H)
3. R  (H • B)
Group of answer choices
R 1, DN
(R  J) • H 2, Assoc
H • B 1, 3, MP
J • H 1, 2, DS
R  (J  H) 2, DM
Question 32
Given the following premises:
1. (F • M)  (L • G)
2. P  L
3. (L • G)
Group of answer choices
L  G 3, DM
(F • M) 1, 3, MT
L  P 2, Trans
P 2, 3, MT
L 3, Simp
Question 33
Given the following premises:
1. S  (T • C)
2. (S • Q)  C
3. C
Group of answer choices
S • Q 2, 3, DS
S  (T • C) 1, DN
S 2, Simp
S  T 1, Simp
S  (T • C) 1, DN
Question 34
Given the following premises:
1. (H • J)  K
2. (H • J)
3. (H • N)  (H • J)
Group of answer choices
H  (J  K) 1, Exp
H • (N  J) 3, Dist
(H • N)  K 1, 3, HS
H • N 2, 3, DS
H  J 2, DM
Question 35
Given the following premises:
1. R  (B  F)
2. U  B
3. B
Group of answer choices
F 1, 3, MP
R  (F  B) 1, Trans
(R  B)  F 1, Assoc
U 2, 3, MT
B  U 2, Trans
Question 36
Given the following premises:
1. T  S
2. A  T
3. A • (T • S)
Group of answer choices
S 1, 3, DS
T  A 2, Com
(A • T) • S 3, Assoc
T 3, Simp
T 2, 3, MP
Question 37
Given the following premises:
1. P
2. L  (P  M)
3. (P • M)  (R  R)
Group of answer choices
L  (R  R) 2, 3, HS
P 3, Simp
M 1, 2, DS
(P • M)  R 3, Taut
(L  P)  (L  M) 2, Dist
Question 38
Given the following premises:
1. N  H
2. Q  (N  H)
3. (N  Q) • (H  Q)
Group of answer choices
Q  Q 1, 3, CD
Q 1, 2, MT
Q  (N • H) 2, DM
N  (N  H) 2, 3, HS
H  Q 3, Simp
Question 39
Given the following premises:
1. R  (E • D)
2. R • G
3. E  G
Group of answer choices
E  G 3, Impl
G 2, Simp
(R • G)  F 2, Add
E 2, 3, MT
E • D 1, 2, MP
Question 40
Given the following premises:
1. (L  M) • (F  J)
2. M  (F  L)
3. F  L
Group of answer choices
L  M 1, Simp
L  (F  L) 1, 2, HS
M  (F  L) 2, DM
M 2, 3, MT
M  J 1, 3, CD

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