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Question 1061899: how to solve using indirect proof when there is a conditional in the conclusion
1. (AvD) -> M
2. ~(BvO)
3. R<->(O.T)
4. ~R<->A :. ~(M->O)

Click here to see answer by Edwin McCravy(20054)

Question 1061816: A>C
(A*C)>H
_______
A>H
Click here to see answer by Edwin McCravy(20054)

Question 1063914: Tim spins a spinner that has red, blue,and yellow sections twice. How many different outcomes are possible?
Click here to see answer by Fombitz(32388)

Question 1065169: Two Column and flow proof. Given:

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Question 1066422: write a direct proof using the eight rules of inference
(C → Q) � (~L → ~R), (S → C) � (~N → ~L), ~Q � J, ~Q → (S v ~N), therefore, ~R
i have to use the eight rules, but this particular problem is very hard for me. hoping you can help.
this is from the power of logic 5th edition.
these are the rules im being given.

Rule 1: Modus ponens (MP): p → q
p
∴ q
Rule 2: Modus tollens (MT): p → q
∼q
∴ ∼q
Rule 3: Hypothetical syllogism (HS): p → q
q → r
∴ p → r
Rule 4: Disjunctive syllogism (DS), in two forms:
p ∨ q p ∨ q
∼p ∼q
∴ q ∴ p
Rule 5: Constructive dilemma (CD): p ∨ q
p → r
q → s
∴ r ∨ s
Rule 6: Simplification (Simp), in two forms:
p � q p � q
∴ p ∴ q
Rule 7: Conjunction (Conj): p
q
∴ p � q
Rule 8: Addition (Add) in two forms:
p p
∴ p ∨ q ∴ q ∨ p

Click here to see answer by Edwin McCravy(20054)

Question 1066635: write a direct proof using the eight rules of inference
~M, (~M � ~N) → (Q → P), P → R, ~N, therefore, Q → R
Thank you in advance
Click here to see answer by solver91311(24713)

Question 1067206: Hello team, would you be so kind to assist with this problem below. I�ve tried to figure out but was wrong. some help is greatly appreciated!
use one of the indirect proof techniques (reduction ad absurdum or conditional proof RAA) to demonstrate the validity of the argument -

(G � P) → K, E → Z, ~P → ~ Z, G → (E v L), therefore, (G � ~L) → K

Click here to see answer by Edwin McCravy(20054)

Question 1067805: ABCD is a parallelogram inscribed in a circle then prove that ABCD is a rhombus
Click here to see answer by ikleyn(52777)

Question 1068315: I do not even know where to start with this proof.
Prove or disprove: let a, b, and c be integers such that a and b are relatively prime and c divides a+b. Prove that gcd(a,c)=gcd(b,c)=1.
Click here to see answer by ikleyn(52777)

Question 1068517: 1. ~(H ⊃ ~E) ⊃ K
2. M v (O ⊃ H)
3. A ⊃ [~A v (~M ⊃ ~K)]
4. A
5. A ⊃ ~M / O ⊃ ~E
Click here to see answer by Apples_21(13)

Question 1069607: I am needing help with this proof. I am very confused.
Prove or disprove: for every natural number n,
1^3+3^3+5^3+...+(2n-1)^3=n^2(2n^2-1).
Click here to see answer by ikleyn(52777)

Question 1070285: Prove that for any integer n, is divisible by 12.
Below is my attempt at trying to solve it, however I don't think example is enough to show as proof.
we want to prove . I written it also as
which if you plug in 2 or 3 it will give an even number in the numerator which means it can be divisible by 12.
Click here to see answer by ikleyn(52777)

Question 1070276: Show that if n is odd integer, then n^3-n is a multiple of 24.
Click here to see answer by ikleyn(52777)

Question 1070276: Show that if n is odd integer, then n^3-n is a multiple of 24.
Click here to see answer by Edwin McCravy(20054)

Question 1070272: Show that if x and y are positive rational numbers with x < y then there is a rational number r with x < r < y.
Click here to see answer by ikleyn(52777)

Question 1070277: For any integer n, prove that
1) 3 divides one of the integers n, n + 1 or 2n + 1.
2) 3 divides one of n, n + 2 or n + 4.
3) 3 divides one of n, 2n - 1 or 2n +1.
Click here to see answer by ikleyn(52777)

Question 1070274: Prove that the product of two odd numbers is odd, using an indirect proof and a proof by contradiction.
Click here to see answer by josgarithmetic(39617)

Question 1070274: Prove that the product of two odd numbers is odd, using an indirect proof and a proof by contradiction.
Click here to see answer by ikleyn(52777)

Question 1070422: Prove that for any integer n, 5 divides n^5-n.
Click here to see answer by solver91311(24713)

Question 1070422: Prove that for any integer n, 5 divides n^5-n.
Click here to see answer by ikleyn(52777)

Question 1071617: ~P->~D
~D->~F
~P∴~F
Click here to see answer by math_helper(2461)

Question 1071953: please help me solve this: 1.(F v G) > (H & I)
2. I > K
3.~k.: ~F
Click here to see answer by Edwin McCravy(20054)

Question 1071952: please help me solve: 1.D v (S & I)
2.D>S :. S
Click here to see answer by Edwin McCravy(20054)

Question 1073145: Prove that parallelogram is a rhombus if its diagonals bisect at right angles

Click here to see answer by KMST(5328)

Question 1074058: let X IS NOT EQUAL TO 0.let X approach to X be a bijective mapping, define
F=(A subset of X : A=f^-1(B) for some B subset of X)
is F a sigma-algebra over X? if so prove. if not,state and show that which property is not satisfied.
Click here to see answer by ikleyn(52777)

Question 1074715: Prove or disprove the statements below.
(a) For all positive real numbers x and y, ⌊x*y⌋ ≤ ⌊x⌋*⌊y⌋
(b) For all positive real numbers x and y, ⌈x*y⌉ ≤ ⌈x⌉*⌈y⌉
I am not sure where to start, could someone please give me some hints on how to solve these kind of question. Thank you in advance.
Click here to see answer by Edwin McCravy(20054)

Question 1074892: Show that if am b, k and m are integers such that k≥1, m≥2, and a≡b( mod m), then a^k≡b^k( mod m)
Click here to see answer by rothauserc(4718)

Question 1074891: determine whether it is valid or invalid. If valid then give a proof. If invalid then give a counter example.
A⊆B ⇒(B)^c⊆(A)^c. Where ()^c means complement.
Click here to see answer by ikleyn(52777)

Question 1075409: Two-step proof
1. ~C
2. A > B
3. B > C / ~A

Click here to see answer by Edwin McCravy(20054)

Question 1075501: Two step proof:
1. A * B / A v C

Click here to see answer by Edwin McCravy(20054)

Question 1075506: Two step proof:
1. (H v I) > J
2. H / J

Click here to see answer by Edwin McCravy(20054)

Question 1075500: Two step proof:
1. D > E
2. F > G
3. D v F / E v G

Click here to see answer by Edwin McCravy(20054)

Question 1075211: Solve the two step proofs below:
1. ~C
2. A > B
3. B > C / ~A
1. D > E
2. F > G
3. D v F / E v G
1. A * B / A v C
1. (H v I) > J
2. H / J
1. (H * I) > J
2. H
3. I / J
1. H > (I * J)
2. H / J
1. (K * L) v (M * N)
2. ~(K * L) / N
Click here to see answer by Edwin McCravy(20054)

Question 1075517: Two step proof:
1. (H * I) > J
2. H
3. I / J

Click here to see answer by Edwin McCravy(20054)

Question 1076080: Using the rules of implication and replacement, the proofs for the following problems. justifications for each step
1. Mv(D�L)
2. B⊃~(MvL) /~B
Click here to see answer by Edwin McCravy(20054)

Question 1076523: Give the equivalence classes of the relation aRb if and only if a^4≡b^4(mod30) on the set {1,2,3,�,15}?
Click here to see answer by ikleyn(52777)

Question 1076492: Please help me show F⊃G follows from [(LvW)*G)]≡F
using the conditional proof.
Click here to see answer by Edwin McCravy(20054)

Question 1076756: If the question is:"State and verify the De Morgan's law if U={1,2,3,4,5,..........,30}",and the given set is "U=Z(set of integers)".What will the solution be? kindly help me understand and solve this question.
Click here to see answer by rothauserc(4718)

Question 1076912: explain how you know that 3^7+2 is an odd number
3^7 is 2187 add 2 is 2189 how do you prove?
prove that the product of two odd numbers is always odd
7*7=49 how do you prove?
Click here to see answer by Alan3354(69443)

Question 1078007: IF BOX 1 - BOX 2 = 9 , BOX3 - BOX4 = 14 , BOX1 + BOX3 =12 , BOX2 +BOX4 = 2 .
FILL THE BOXES.
Can you answer this for me. I'm really tired figuring it out.

Click here to see answer by ikleyn(52777)

Question 1078186: Need help writing out this proof using induction and elimination rules.
(E V B) --> ~D
S V D
E
goal: S
also:
(P ^ ~Q) --> ~(P <-> Q)
Prove goal without premises
Click here to see answer by Edwin McCravy(20054)

Question 1079374: Can you help me with this assignment in analytic geometry:
Find the distance of the point (12,7) from the line through (5,3) and (2,-3)
I need a complete solution. Thank you!
Click here to see answer by ikleyn(52777)

Question 1079391: Can you help me with this assignment in analytic geometry:
Three consecutive vertices of a parallelogram are (1,-3); (-3,-1) and (3,5). Find the 4th vertex.
I need a complete solution. Thank you!
Click here to see answer by Edwin McCravy(20054)

Question 1079560: Can you help me with this assignment in analytic geometry:
Draw a line through the points (-4,-5) and show that the slope is -2/3
I need a complete solution. Can you graph it. Thank you!
Click here to see answer by josgarithmetic(39617)

Question 1079559: Can you help me with this assignment in analytic geometry:
Find the equation of the ꓕ bisector of the line joining the pts J (6,4) and K (4,-2)
I need a complete solution. Can you graph it. Thank you!
Click here to see answer by josgarithmetic(39617)

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