Tutors Answer Your Questions about Proofs (FREE)
Question 548064: Prove that the function is bijective. The function is f: N--->Z f(x)=(1+(−1)^x * (2x − 1)) /4
I tried to attempt it using induction. I did a base case for subjectivity of f(1) and f(2) and it worked. Then I tried to substitute k+1 for x but I have gotten stuck.
Click here to see answer by richard1234(7193)   |
Question 551411: Given:
If schools close, then workers will lose their jobs
If we save fuel, then workers will not lose their jobs
We save fuel or there is an energy crisis
Schools will close
PROVE: There is an energy crisis
Click here to see answer by Theo(13342)  |
Question 562200: There is a famous theorem in Euclidean geometry that states that the sum of
the interior angles of a triangle is 180.
(a) Use the theorem about triangles to determine the sum of the angles of
a convex quadrilateral.
(b) Use the result in Part (1) to determine the sum of the angles of a convex
pentagon.
(c) Use the result in Part (2) to determine the sum of the angles of a convex
hexagon.
Click here to see answer by richard1234(7193) |
Question 563757: Can you please help me with this probability question...
A person spins the pointer and is awarded the amount indicated by the pointer.
It costs $5 to play the game. The diagram shows a circle divided into 3 parts. The pointer points to the 1/2 section marked $2. The 1/4 section is marked $20, and the other 1/4 section is marked $5.
Determine:
The expectation of a person who plays the game.
The fair price to play the game.
Click here to see answer by stanbon(75887) |
Question 567801: Proposition 1.8
If m is an integer, then (-m)+m=0
Proof
Let m be an element of Z
There exist a (-m) in an element Z Axiom 1.4
such that m+(-m)=0
m+(-m) = (-m)+m Axiom 1.1(i)
= 0 Q.E.D
That's how I assume it is proven but it would be nice if someone could double check and make sure it is correct and also correct it. Thanks
Click here to see answer by richard1234(7193) |
Question 571456: Each student at Sussex Elementary School takes one foreign language. Two thirds of the students take Spanish, 1/9 take French, 1/18 take German, and the rest take some other foreign language. if there are 720 students in the school, how many do not take Spanish, French, and German?
Click here to see answer by josmiceli(19441)  |
Question 574686: Decide whether or not the following proposition is true. If it is false, demonstrate this by presenting a counterexample. If it is true, decide whether or not the proof is correct. If the proof is not correct, rewrite the proof so that it is correct. If the proof is correct, decide whether or not it is well-written and revise the proof, as needed, so that it is well-written.
Proposition. For each natural number n with n > 2, it is true that 2n > 1 + n.
Proof. We let k be a natural number and assume that 2k > 1 + k. Multiplying both sides of this inequality by 2, we see that 2k+1 > 2 + 2k. However, 2 + 2k > 2 + k, and hence,
2k+1 > 1 + (k + 1).
By mathematical induction, we conclude that 2n > 1 + n.
Click here to see answer by solver91311(24713)  |
Question 574686: Decide whether or not the following proposition is true. If it is false, demonstrate this by presenting a counterexample. If it is true, decide whether or not the proof is correct. If the proof is not correct, rewrite the proof so that it is correct. If the proof is correct, decide whether or not it is well-written and revise the proof, as needed, so that it is well-written.
Proposition. For each natural number n with n > 2, it is true that 2n > 1 + n.
Proof. We let k be a natural number and assume that 2k > 1 + k. Multiplying both sides of this inequality by 2, we see that 2k+1 > 2 + 2k. However, 2 + 2k > 2 + k, and hence,
2k+1 > 1 + (k + 1).
By mathematical induction, we conclude that 2n > 1 + n.
Click here to see answer by richard1234(7193) |
Question 588387: I am trying to work on the following proof. I know I used DEM incorrectly on line 3. I cannot figure out what other rule to use. I tried contraposition, but it does not allow me to break down the lines. I cannot use MT or MP without having x or y by itself. I do not know what other conditional rule to use.
1. X > Y / X . Z > Y
2. ~X v Y CE 1
3. ~X . ~Y DEM 3
4. ~X Simp 3
5. ~Y Simp 3
6. X DS 2,5
7. Y DS 2,4
8 X v Z Add 6
9. Z DS 4,8
10. ~X v Z Conj 4,9
11. X > Z CE 10
12. ~Z > ~X Contrap 11
13. ~Z MT 4,12
14. ~Z v Y Add 13
15. Z > Y CE 14
16. X . Z > Y Conj 6,15
thank you!
Click here to see answer by jim_thompson5910(35256) |
Question 592846: INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises.
Given the following premises:
1. ~N v H
2. Q > ~(~N v H)
3. (~N v Q) • (H > Q)
A. Q v Q 1, 3, CD
B. ~Q 1, 2, MT
C. ~N > ~(~N v H) 2, 3, HS
D. Q > (N • ~H) 2, DM
E. H > Q 3, Simp
Click here to see answer by jim_thompson5910(35256) |
Question 592849: INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises.
Given the following premises:
1. Q > (H • L)
2. H > ~Q
3. L > ~Q
A. Q > ~Q 1, 3, HS
B. (L > ~Q) • (H > ~Q) 2, 3, Conj
C. (Q > H) > L 1, Exp
D. H > L 2, 3, HS
E. L > (H • L) 1, 3, HS
Click here to see answer by jim_thompson5910(35256) |
Question 607200: Could you please help me solve the following proof? I have worked a few lines after the conclusion but am stuck after that.
1. E>(S>T)
2. (~L*M) > (S*E)
3. ~(TvL) // ~M
4. (E*S) >T 1. Exportation
5. ~T*~L 3. DeMorgans
6. ~T 5. Simplification
7. ~(E*S) 4,6 Modus Tollens
Key: > equals wedge
* equals dot
Click here to see answer by jim_thompson5910(35256) |
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