Advanced Mathematics
Name: ___________________
1.
Determine the truth-values of the following symbolized statements. Let A, B, and C be true; G, H, and K,
false; M and N, unknown truth-value.
2.
a.
A • ∼G
b.
∼A ∨ G
c.
∼(A ⊃ G)
d.
∼G ≡ (B ⊃ K)
e.
(A ⊃ ∼C) ∨ C
f.
B • (∼H ⊃ A)
g.
M ⊃ ∼G
h.
(M ∨ ∼A) ∨ H
i.
(N • ∼N) ≡ ∼K
j.
∼(M ∨ ∼M) ⊃ N
Use a truth table to decide whether each of the following symbolized statements is tautologous, selfcontradictory or contingent.
3.
Logic
11-27-16
a.
D ⊃ (B ∨ ∼B)
b.
K • (∼M ∨ ∼K)
c.
(S ⊃ H) ≡ (∼H • S)
d.
(R ⊃ E) ∨ ∼H
e.
(N • ∼(D ∨ ∼E)) ≡ D
Use truth tables to determine whether each pair of statements are logically equivalent, contradictory,
consistent, or inconsistent.
a.
G • ∼D
D ∨ ∼G
b.
∼(M ⊃ B)
∼B • ∼M
c.
∼A ≡ C
(A • ∼C) ∨ (C • ∼A)
d.
J ⊃ ∼(L ∨ N)
(∼L ⊃ N) • J
e.
∼((E ⊃ K) • ∼O)
O ∨ (E • ∼K)
f.
∼(H ∨ ∼(R • S))
(∼S • R) ⊃ ∼H
4.
Symbolize the arguments and then use the truth table to decide whether they are valid.
a.
∼(A ∨ B)
∼A ⊃ B
∼B
b.
∼E ∨ (G ≡ E)
∼(E • G)
∼G
c.
P ⊃ ∼D
(∼R ⊃ D) ∨ P
R⊃P
d.
∼(S ∨ C)
(S • C) ⊃ ∼H
C⊃H