Questions on Logic: Proofs answered by real tutors!

Tutors Answer Your Questions about Proofs (FREE)

Question 1179695: INSTRUCTIONS: Use natural deduction to derive the conclusion in each problem.
Prove this using natural deduction.

NOTE: Use * for dot, v for wedge, ~ for tilde, = for triple bar (or copy and paste ≡), and > for horseshoe (or copy and paste ⊃ )

1. M ⊃ (∼B ⊃ J)
2. B ⊃ (~M * ~M)
3. ∼J / ~M
Click here to see answer by RBryant(14)

Question 1156253: 1. (F v G) ⊃ ~A
2. A v W
3. F • T /∴ W

Click here to see answer by RBryant(14)

Question 1203590: Andaikan ABCD trapesium, E titik tengah kaki AD dan F titik tengah kaki BC. Buktikan bahwa EF=1/2(AB+DC)
Click here to see answer by MathLover1(20849)

Question 1203590: Andaikan ABCD trapesium, E titik tengah kaki AD dan F titik tengah kaki BC. Buktikan bahwa EF=1/2(AB+DC)
Click here to see answer by ikleyn(52778)

Question 1203591: Ada sebuah jajaran genjang. Titik-titik tengah dua sisi yang berhadapan dihubungkan dengan titik-titik sudutnya,maka terdapat suatu jajaran genjang baru yang diagonal-diagonalnya sejajar dengan sisi-sisi jajaran genjang yang diketahui. Sedangkan panjangnya salah satu diagonalnya sama dengan sebuah panjang sisi jajaran genjang yang diketahui dan panjangnya yang lain sama dengan setengah panjang sisi jajaran genjang yang lain. Buktikan
Click here to see answer by Edwin McCravy(20054)

Question 1204059: Prove this with steps please
1 [(A v ~B) v T]->(X->M)
2 (A v R)->(Z->O)
3 A&(X v Z)
4 (M v O)->(A->E)
5 ~E&S
//∴H=K
Click here to see answer by Edwin McCravy(20054)

Question 1204115: please solve these problems with steps:
_______________________
1. ~(K v A) > (R v W)
2. ~K
3. ~A /∴ R v W
_______________________
1. A v ~(O v M)
2. B > ~(A v ~M) /∴ ~B
_______________________
1. (Z + ~A) v (B > Z)
2. ~Z /∴ ~B
_______________________
1. ~A
2. ~Z /∴ ~[(A v Z) + B]

Thank you!!!

Click here to see answer by Edwin McCravy(20054)

Question 1204165: please solve:
1. (K v S) v (T v W)
2. ~S + [T v ~(O v Z)]
3. K > ~(T v ~Z) /∴ T v W

1. (A > O) v (Z + ~T)
2. ~Z + ~O /∴ ~[(A v Z) + K]
Click here to see answer by Edwin McCravy(20054)

Question 1204214: ~p ^ r
p v q
--------
∴ q v r
Click here to see answer by math_tutor2020(3816)

Question 1204272: solve plz? with rules of inference and replacement...
1. (~D + A) v (~D + R)
2. D v ~A /∴ K > R
_______________________________
1. ~(G + M)
2. M v ~G /∴ ~G
_______________________________
I know y'all only answer two questions...but it's worth a shot to ask...If not, thank you anyways!!
1. P = (R + S)
2. P /∴ R = S

Click here to see answer by math_tutor2020(3816)

Question 1204425: 1). ~(K•L)
2). K -> L
Therefore, ~K
Click here to see answer by Edwin McCravy(20054)

Question 1204425: 1). ~(K•L)
2). K -> L
Therefore, ~K
Click here to see answer by math_tutor2020(3816)

Question 1204566: Prove using Inference and Replacement Rules:
1). Q -> R
2). R -> S
3). ~S
Therefore, Q • ~R
Click here to see answer by math_tutor2020(3816)

Question 1204701: Use conditional proof (CP) together with the eight rules of implication and ten rules of replacement to prove that they are valid. Be sure to include the justification for each line, and offset lines as appropriate for conditional proof.
1. A ⊃ (B ⊃ (C • ~D))
2. (B v E) ⊃ (D v E) /(A • B) ⊃ (C • E)

Click here to see answer by math_tutor2020(3816)

Question 1204702: Use indirect proof (IP) together with the eight rules of implication and ten rules of replacement to prove that they are valid. Be sure to include the justification for each line, and offset lines as appropriate for indirect proof.
1. C ⊃ (N • I)
2. (N v P) ⊃ (I ⊃ ~C) /~C

Click here to see answer by math_tutor2020(3816)

Question 1204739: Use all eighteen rules
1. Q ⊃ (F ⊃ A)

2. R ⊃ (A ⊃ F)
3. Q • R / F ≡ A

Click here to see answer by math_tutor2020(3816)

Question 1205072: Use all 18 rules
1. ∼(U ● W ) ⊃ X
2. U ⊃ ∼U / ∼(U v ∼X )

Click here to see answer by math_tutor2020(3816)

Question 1205222: Proving [F • (D ⊃ ∼F)] ⊃ (D ⊃ A) using the eighteen logical rules of inference
Click here to see answer by math_tutor2020(3816)

Question 1205227: Use natural deduction to derive the conclusion in each problem.

Use conditional proof:

1. S ⊃ (B ⊃ T)
2. N ⊃ (T ⊃ ∼B) / (S • N) ⊃ ∼B
Click here to see answer by math_tutor2020(3816)

Question 1205245: 1. J v (K · L)
2. ~ K //  J

Click here to see answer by Edwin McCravy(20054)

Question 1205245: 1. J v (K · L)
2. ~ K //  J

Click here to see answer by math_tutor2020(3816)

Question 1205405: 1. C ⊃ (D v A) /~C v D
2. A ⊃ H
3. ~H
Click here to see answer by mccravyedwin(406)

Question 1205405: 1. C ⊃ (D v A) /~C v D
2. A ⊃ H
3. ~H
Click here to see answer by Edwin McCravy(20054)

Question 1205226: Use natural deduction to derive the conclusion in each problem.

Use natural deduction to prove the following logical truth:
(P ⊃ Q) ≡ [P ⊃ (Q ∨ ∼P)]
Click here to see answer by math_helper(2461)

Question 1206424: Premise:
1.
(K ∨ L) ⊃ (M • N)
2.
(N ∨ O) ⊃ (P • ~K)
Conclusion:
~K
Use either indirect proof or conditional proof (or both) and the eighteen rules of inference to derive the conclusion of the following symbolized argument.
Click here to see answer by math_tutor2020(3816)

Question 1206425: Premise:
1.
F
Conclusion:
(G ⊃ H) ∨ (~G ⊃ J)
Use either indirect proof or conditional proof (or both) and the eighteen rules of inference to derive the conclusion of the following symbolized argument.
Click here to see answer by Edwin McCravy(20054)

Question 1206856: 1. (I&-E) -> -I |-(Conclusion) I -> E
Click here to see answer by Edwin McCravy(20054)

Question 1206984: D ⊃ E
2. D v A
3. ~E / A

Click here to see answer by Edwin McCravy(20054)

Question 1206984: D ⊃ E
2. D v A
3. ~E / A

Click here to see answer by mccravyedwin(406)

Question 1206984: D ⊃ E
2. D v A
3. ~E / A

Click here to see answer by math_tutor2020(3816)

Question 1207017: PLease use all 18 rules of natural deduction to derive the conclusion (/), thanks.
1. S ⊃ (L • M)
2. M ⊃ (L ⊃ R) / S ⊃ R
Click here to see answer by mccravyedwin(406)

Question 1207017: PLease use all 18 rules of natural deduction to derive the conclusion (/), thanks.
1. S ⊃ (L • M)
2. M ⊃ (L ⊃ R) / S ⊃ R
Click here to see answer by math_tutor2020(3816)

Question 1207022: please use all 18 rules of natural deduction to derive the conclusion (/), thanks.
1. T ⊃ R
2. T ⊃ ~R / ~T
Click here to see answer by math_tutor2020(3816)

Question 1207211: Can you please help me solve the following trigonometry exact values with working out:
sin 2pi/3
cos 3pi/4
tan 5pi/6
sin 7pi/6
cos 5pi/4
tan 4pi/3
sin 5pi/3
cos 7pi/4
tan 11pi/6
I know it is a lot of questions to ask but I am quite stuck. It would be nice if all of them are complete but if this is too much to ask for atleast half to 3/4s of them would be nice. Thankyou!
Click here to see answer by Theo(13342)

Question 1207462: Hi there, I'd love some help on answering these Logic Proof Questions:
1.
1. T > O
2. R v ~O
3. ~R/~T
2.
1. (Q ~J) (M ~D)
2. Q M
3. M ~J/Q ~D

3.
1. T (Q & F)
2. T & C/Q v O

4.
1. F ~U
2. ~F P
3. F v ~F/~U v P
5.
1. (J v F) v M
2. (J v M) ~P
3. ~F/~(F v P)
6.
1. (A> B) > (C & D)
2. C ~D/~A
7.
1. (A & B) C
2. B & ~C/~A
8.
1. A v B
2. A ≡ (C & D)
3. B

Click here to see answer by math_tutor2020(3816)

Question 1207464: Hello, may I please get some help on these proofs? Thank you in advance! :)

https://ibb.co/HhS7QHM

Click here to see answer by Edwin McCravy(20054)

Question 1207463: Hi, how do I solve these two Proofs?
https://ibb.co/r5XF5dS
Click here to see answer by math_tutor2020(3816)

Question 1207196: Please use the 18 rules of natural deduction, the 4 instantiation and generalization rules to derive the conclusion of the problem
1. (x)[Ax ⊃ (Bx ∨ Cx)]
2. Ag • ~Bg / Cg
Click here to see answer by Edwin McCravy(20054)

Question 1207571: P) A or B
P) Not A & Not C
Therefore B
Must be solved using rules of inference
Click here to see answer by math_tutor2020(3816)

Question 1207644: Given the argument:
1. G⊃(H⊃K)
2.(H∨∼M)⊃∼K
3. H /∼G
Identify the rules of replacement/inference used to derive the proposition: (G • H) ⊃ ~K?
Click here to see answer by Edwin McCravy(20054)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485