Questions on Logic: Proofs answered by real tutors!

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Question 1009274: Can you please help me solve this proof? I am stuck at line six.
1. (A → E) → (D ∨ C)
2. D → (~B → C) ∴ ~C → (A ∨ B)
|3. ~C Assume
||4. ~A Assume
||5. (D∙~B)→C 2, EX
||6.
Click here to see answer by jim_thompson5910(35256)

Question 1009333: Derive:(~P) v Q
1. P>Q
Click here to see answer by jim_thompson5910(35256)

Question 1009334: Derive: A v ~B
1.(F v G) v (A v ~B)
2. F>A
3. B>~G
Click here to see answer by jim_thompson5910(35256)

Question 1009356: Given: P: ABC is an equilateral triangle
Prove: r: AB=BC=CA
Click here to see answer by ikleyn(52775)

Question 1009889: 1. (P v F) -> (A v D)
2. A -> (M ^ ~P)
3. D -> (C ^ ~P) / ~P
Click here to see answer by Edwin McCravy(20054)

Question 1009931: Very confused with this proof, any help would be appreciated!!
Conditional Proof - can use all 18 rules
P -> (~P -> (Q <-> (R v S)))

Click here to see answer by jim_thompson5910(35256)

Question 1009929: Natural Deduction - all 18 rules can be used
1. M -> (R ^ E)
2. (E v H) -> G / M -> G
Click here to see answer by jim_thompson5910(35256)

Question 1009930: Conditional Proof - can use all 18 rules
(P -> Q) <-> (P -> (Q v ~P))
Click here to see answer by jim_thompson5910(35256)

Question 1009886: 1. M -> (R ^ E)
2. (E v H) -> G /M -> G
Click here to see answer by Edwin McCravy(20054)

Question 1010073: H -> U // H -> (U v T)
Click here to see answer by jim_thompson5910(35256)

Question 1010046: Can i please have help solving these proofs?
Use an ordinary proof (not conditional or indirect proof):
1. A ⊃ (Q ∨ R)
2. (R � Q) ⊃ B
3. A � ∼B / R ≡ ∼Q
a regular proof to derive the conclusion of the following argument:
1. (A & U) < > ~R
2. ~(~R v ~A) / ~U
a regular proof to derive the conclusion of the following argument:
1. X >Y
2. (Y v ~X) > (Y > Z) / ~Z > ~X
Click here to see answer by jim_thompson5910(35256)

Question 1010045: can i have help solving these proofs
a regular proof to derive the conclusion of the following argument:
1. C
2. (C & T) > ~T
3. (C & ~T) > T / T < > ~T
a regular proof to derive the conclusion of the following argument:
1. N > R
2. O <> R
3. (O > R) > L / (N > O) & L
a regular proof to derive the conclusion of the following argument:
1. H v (~T > R)
2. Hv (E > F)
3. ~T v E
4. ~H & D / R v F
Click here to see answer by jim_thompson5910(35256)

Question 1010096: 1. (G->J)->(G->Q)
2. J*~Q
//~H
Click here to see answer by jim_thompson5910(35256)

Question 1010296: can i have help with these two proofs?
1. X >Y
2. (Y v ~X) > (Y > Z) / ~Z > ~X
Click here to see answer by Edwin McCravy(20054)

Question 1010505: can i have help solving this proof please?
Construct a regular proof to derive the conclusion of the following argument:
1. H v (~T > R)
2. Hv (E > F)
3. ~T v E
4. ~H & D / R v F
Click here to see answer by jim_thompson5910(35256)

Question 1010841: I am preparing for my final and am stuck studying on this problem. Please help me by doing a formal proof for each line and the rule.
1. ~B&R
2. R⊃~(MvP)
3. (N⊃S)⊃~I
4. N⊃L
5. E⊃(S≡L)
6. E /.: ~I&~M
Click here to see answer by Edwin McCravy(20054)

Question 1010735: INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. H v (~T > R)
2. Hv (E > F)
3. ~T v E
4. ~H & D
/ R v F
Click here to see answer by Edwin McCravy(20054)

Question 1010733: INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. C
2. (C & T) > ~T
3. (C & ~T) > T / T < > ~T
Click here to see answer by Edwin McCravy(20054)

Question 1010734: INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. N > R
2. O <> R
3. (O > R) > L
/ (N > O) & L
Click here to see answer by jim_thompson5910(35256)

Question 1010727: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems.
Use an ordinary proof (not conditional or indirect proof):
1. A ⊃ (Q ∨ R)
2. (R � Q) ⊃ B
3. A � ∼B
/ R ≡ ∼Q

Click here to see answer by jim_thompson5910(35256)

Question 1010728: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems.
Use indirect proof:
1. (R ∨ S) ⊃ (H � ∼G)
2. (K ∨ R) ⊃ (G ∨ ∼H)
/ ∼R
Click here to see answer by jim_thompson5910(35256)

Question 1011127: A seller allows a discount of 5% on watch.
if it discounts at 7% he earns Rs.15 less in profit. What is the MP;
Click here to see answer by Theo(13342)

Question 1010731: INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. (A & U) < > ~R
2. ~(~R v ~A)
/ ~U
Click here to see answer by Edwin McCravy(20054)

Question 1010732: Construct a regular proof to derive the conclusion of the following argument:
1. X >Y
2. (Y v ~X) > (Y > Z)
/ ~Z > ~X
Click here to see answer by Edwin McCravy(20054)

Question 1011177: I need to help on the following proofs
Proof 1
B ∧ F
�(B ∧ G)
------
�G
Proof 2
Goal - [A → (B →C)] ↔ [(A → B) → (A → C)]
Proof 3
∃x (A(x) ∨ B(x))
∃x A(x) → ∀x (C(x) → B(x))
∃x C(x)
Goal ∃x B(x)
Click here to see answer by Edwin McCravy(20054)

Question 1011444: 11)
1)A→(B→C)
2) ~C
3) ~D→A
4)C v~D

Conclusion should by ~B, needs to be solved by using MP,MT,DS or,HS

Click here to see answer by jim_thompson5910(35256)

Question 1011026: Complete the following derivation: --THANK YOU!! THIS IS MUCH NEEDED
1. ~[∀x: Ax] Bx
2. [∀x: [∃y: Ay] Rxy] [∃z: Bz] Rxz
3. [∀x: Ax ● ~Bx] [∃y: Cy] Ryx

∴ [∃y: Cy] [∃z: Bz] Ryz
Click here to see answer by addingup(3677)

Question 1015116: if a student were paid .25 for each math test taken, and was fined .50 for each failed math test; and he passed 7x's as many tests as he failed. How many tests did he fail, if he was paid $3.75?
Click here to see answer by stanbon(75887)

Question 1015261: similarities between, 87,17,19,4,2.
Click here to see answer by ikleyn(52775)

Question 1015261: similarities between, 87,17,19,4,2.
Click here to see answer by Alan3354(69443)

Question 1016956: When A ⊆ B the difference B \ A is defined to be the set of all objects that are in A but not in B.
Construct a counterexample to the statement �Given A ⊆ B ⊆ C, C \ (B \ A) = (C \ B) \ A�.
Click here to see answer by richard1234(7193)

Question 1016954: Let Dn denote the set of natural numbers that divide n exactly. For example,
D60 = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}.
Write down the sets D84 and D60 ∪ D84. Find the number m such that Dm = D60 ∪ D84. Is it true that for any natural numbers r and s there is a natural number m such that Dm = Dr ∪ Ds?

Click here to see answer by richard1234(7193)

Question 1016952: List all elements of the set A ∩ B, where A = {n ∈ N | n = 2^n − 1} and B{n ∈ N | n = 2^n + 3}.
Click here to see answer by richard1234(7193)

Question 1019873: By giving a proof or a counterexample, determine the truth value of the following
statement.
For every pair of natural numbers x and y such that x > 2y there is a natural number z such that
x > z > y.

Click here to see answer by LinnW(1048)

Question 1019877: The natural numbers 1 ≤ n ≤ 25 are arranged in a square array of five rows and five
columns in an arbitrary manner. The greatest member of each row is selected and s denotes the least
of these. Similarly, the least member in each column is selected and t denotes the greatest of these.
Construct an example in which s not equal to t, and show that s ≥ t always. [Hint: Find x such that s ≥ x and
x ≥ t.]

Click here to see answer by richard1234(7193)

Question 1020241: Prove that 3 divides 20^2n − 1 for all n = 0, 1, 2, 3, . . ..
Click here to see answer by Fombitz(32388)

Question 1021209: The sequence u_n is defined recursively by the rules
u_1 = 3, u_2 = 3, u_(n+2) = u_(n+1) + 2u_n for all n ∈ N.
Find the formula for the general term of the sequence and prove it.

Click here to see answer by richard1234(7193)

Question 1021206: Prove that n^5 − n is divisible by 5 for any natural n
Click here to see answer by richard1234(7193)

Question 1021264: if x and y are odd numbers, then x+y is even
If x and y are both odd, then x+1 and y-1 are even. But then x+y=(x+1)+(y-1) is the sum of two even numbers, and, therefore, even.
Is this a valid proof? If so, what type of proof is it because I am confused.
Click here to see answer by stanbon(75887)

Question 1021450: Let f_n be the nth Fibonacci number. Show that for every natural n
f_1 + f_2 + . . . + f_n = f_(n+2) − 1.
Click here to see answer by richard1234(7193)

Question 1022193: I'm having difficulty solving an exercise.
The question is:
Prove 3^n >=1+2*n. (proving by induction)
Basis step is true n=1 3^1>=1+2*1
I assume n=k is true 3^k>=1+2*k
I now have to prove for n=k+1 ; 3^k+1>=1+2(k+1)
3^k*3^1>=1+2*k+2
This is where I get stuck.
Click here to see answer by richard1234(7193)

Question 1022576: 1. F v (G & S)
2. ~ (I v S) // F & F
Click here to see answer by Edwin McCravy(20054)

Question 1022622: Prove that the two arguments below are valid, using
the method of natural deduction. Use the rules of
implication and rules of replacement
1. B -> (D -> H)
2. ~(D -> ~B) // H

Click here to see answer by Edwin McCravy(20054)

Question 1022311: Prove using induction that: for every non negative integer n, 2^n>n
Click here to see answer by robertb(5830)

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