Chapter 7 L&C quiz
Indirect Proofs always involve
a contradiction
Proofs always end with
a line which states the conclusion of the argument to be proved
in Natural Deduction, a proof is
a series of steps that show the premises lead, by way of valid rules of inference, to the conclusion
The RAA principle is the strategy behind
an indirect proof
The basic purpose of our system of inference rules for Natural Deduction proofs is to show that
any valid argument is valid
In the course materials, Conditional Proof was compared to the idea of
borrowing money
Proofs always begin with
one or more premises or assumptions
Given the following premises: 1.∼T ⊃ E 2. ∼K ⊃ (∼T ∨ ∼T) 3. M ⊃ (∼K ∨ ∼L) Select the conclusion that follows in a single step from the given premises.
M ⊃ (K ⊃ ∼L) 3, Impl
Given the following premises: 1.(S • ∼J) ∨ (∼S • ∼∼J) 2. S ∨ ∼S 3. ∼J ⊃ P Select the conclusion that follows in a single step from the given premises.
S ≡ ∼J 1, Equiv
Given the following premises: 1. (J • ∼N) ∨ T 2. ∼(J • ∼N) 3. ∼T Select the conclusion that follows in a single step from the given premises.
T 1, 2, DS
Can there be more than one correct proof of a valid argument?
Yes
Given the following premises:1. 1. ∼D ∨ ∼T 2. D ∨ (∼T • ∼R) 3. D Select the conclusion that follows in a single step from the given premises.
(D ∨ ∼T) • (D ∨ ∼R) 2, Dist
Given the following premises: 1.Q ⊃ (H • L) 2. H ⊃ ∼Q 3. L ⊃ ∼Q Select the conclusion that follows in a single step from the given premises.
(L ⊃ ∼Q) • (H ⊃ ∼Q) 2, 3, Conj
Given the following premises: 1.(S ⊃ R) ⊃ (J ⊃ T) 2. (P ⊃ R) ⊃ (S ⊃ R) 3. R ⊃ J Select the conclusion that follows in a single step from the given premises.
(P ⊃ R) ⊃ (J ⊃ T) 1, 2, HS
Given the following premises: 1. ∼N • ∼F 2. K ⊃ (N • F) 3. U ∨ (K • ∼N) Select the conclusion that follows in a single step from the given premises.
(U ∨ K) • (U ∨ ∼N) 3, Dist
Given the following premises: 1.F ⊃ J 2. A ⊃ (F • J) 3. A • (Q ∨ N) Select the conclusion that follows in a single step from the given premises.
A • (N ∨ Q) 3, Com
Given the following premises: 1.K ∨ ∼H 2. (K ∨ ∼H) ⊃ (B ⊃ J) 3. J ⊃ D Select the conclusion that follows in a single step from the given premises.
B ⊃ J 1, 2, MP
Given the following premises:1. 1. K ∨ ∼H 2. (K ∨ ∼H) ⊃ (B ⊃ J) 3. J ⊃ D Select the conclusion that follows in a single step from the given premises.
B ⊃ J 1, 2, MP
Given the following premises: 1.(C • ∼F) ⊃ E 2. G ∨ (C • ∼F) 3. ∼(C • ∼F) Select the conclusion that follows in a single step from the given premises.
C ⊃ (∼F ⊃ E) 1, Exp
Given the following premises: 1.N ∨ C 2. (N ∨ C) ⊃ (F ⊃ C) 3. ∼C Select the conclusion that follows in a single step from the given premises.
F ⊃ C 1, 2, MP
Given the following premises: 1. A 2. G ⊃ (A ⊃ ∼L) 3. ∼A ∨ ∼G Select the conclusion that follows in a single step from the given premises.
G ⊃ (∼∼L ⊃ ∼A) 2, Trans
Given the following premises: 1.(K • ∼T) ∨ (K • ∼H) 2. ∼M ⊃ (K • ∼H) 3. ∼(K • ∼H) Select the conclusion that follows in a single step from the given premises.
K • (∼T ∨ ∼H) 1, Dist
Given the following premises: 1. ∼∼N 2. K ⊃ ∼N 3. ∼N ∨ (K • S) Select the conclusion that follows in a single step from the given premises.
K • S 1, 3, DS
Given the following premises: 1.∼∼N 2. K ⊃ ∼N 3. ∼N ∨ (K • S) Select the conclusion that follows in a single step from the given premises.
K • S 1, 3, DS
Given the following premises: 1. G • ∼A 2. K ⊃ (G • ∼A) 3. G ⊃ M Select the conclusion that follows in a single step from the given premises.
K ⊃ ( ∼A • G) 2, Com
Given the following premises. 1.∼M ⊃ S 2. ∼M 3. (M ∨ H) ∨ ∼S Select the conclusion that follows in a single step from the given premises.
M ∨ (H ∨ ∼S) 3, Assoc
Given the following premises: 1.N ≡ R 2. (N • ∼R) ⊃ C 3. N Select the conclusion that follows in a single step from the given premises.
N ⊃ (∼R ⊃ C) 2, Exp
Given the following premises: 1. P • (∼H ∨ D) 2. ∼(∼P • ∼H) 3. (P ⊃ ∼H) • (∼P ⊃ H) Select the conclusion that follows in a single step from the given premises.
P • (H ⊃ D) 1, Impl
Given the following premises: 1. Q ⊃ (A ∨ ∼T) 2. T 3. A ∨ ∼T Select the conclusion that follows in a single step from the given premises.
Q ⊃ (∼∼A ∨ ∼T) 1, DN
Given the following premises: 1.A 2. (A ⊃ ∼T) ⊃ ∼G 3. Q ⊃ (A ⊃ ∼T) Select the conclusion that follows in a single step from the given premises.
Q ⊃ ∼G 2, 3, HS
Given the following premises: 1. ∼R ≡ ∼R 2. N • ∼T 3. R ⊃ ∼(N • ∼T) Select the conclusion that follows in a single step from the given premises.
R ⊃ (∼N ∨ ∼∼T) 3, DM
Given the following premises: 1.R • ∼S 2. R ⊃ ∼(S • ∼F) 3. ∼S ⊃ (F • N) Select the conclusion that follows in a single step from the given premises.
R ⊃ (∼S ∨ ∼∼F) 2, DM
Given the following premises: 1.∼U ⊃ (S • K) 2. R ⊃ (∼U • ∼U) 3. S ≡ ∼U Select the conclusion that follows in a single step from the given premises.
R ⊃ ∼U 2, Taut
'RAA' is an abbreviation for
Reductio ad Absurdum
In the course materials, Indirect Proof was compared to the idea of
troubleshooting a problem with your car battery
The guiding principle of reductio ad absurdum is that
whatever implies a contradiction is false.
Given the following premises: 1.∼I ∨ ∼∼B 2. M ⊃ ∼I 3. I Select the conclusion that follows in a single step from the given premises.
∼(I • ∼B) 1, DM
Given the following premises: 1.N 2. R ⊃ ∼N 3. ∼C • (T ⊃ R) Select the conclusion that follows in a single step from the given premises.
∼C 3, Simp
Given the following premises: 1. D ⊃ H 2. ∼D 3. ~(D • S) Select the conclusion that follows in a single step from the given premises.
∼D ∨ (D ⊃ H) 2, Add
Given the following premises: 1. D ⊃ H 2. ∼D 3. ∼(D ∨ S) Select the conclusion that follows in a single step from the given premises.
∼D ∨ (D ⊃ H) 2, Add
Given the following premises: 1. (S ⊃ ∼F) • (∼F ⊃ B) 2. S ∨ ∼F 3. ∼F Select the conclusion that follows in a single step from the given premises.
∼F ∨ B 1, 2, CD
Given the following premises: 1.∼E ⊃ P 2. ∼P 3. ∼(P ∨ ∼H) Select the conclusion that follows in a single step from the given premises.
∼P • ∼(P ∨ ∼H) 2, 3, Conj
Given the following premises: 1.Q ⊃ (H • ∼F) 2. ∼(Q • ∼M) 3. ∼G ⊃ (Q • ∼M) Select the conclusion that follows in a single step from the given premises.
∼Q ∨ ∼∼M 2, DM
Given the following premises: 1. ∼(Q • ∼S) 2. ∼F ⊃ (Q • ∼S) 3. H ∨ (Q • ∼S) Select the conclusion that follows in a single step from the given premises.
∼∼F 1, 2, MT
