Bridge to abstract math: what is wrong with following proof

In summary, the conversation discusses a question about proving a statement to be true, but the individual proceeds to prove it false. They simplify the given expression and arrive at a contradiction, leading them to believe that their proof is wrong. The conversation then shifts to discussing truth tables and using Wolfram Alpha to check them. It is pointed out that the statement being proved is actually false for certain values of x. The original statement is deemed incorrect due to a mistake made by the professor.
  • #1
Aziza
190
1
See attached picture.

The question asks to prove that the statement which I have written on the first line is true. But I somehow proceeded to proving it is false. Basically what I did was simplify the given expression into the form (P or Q) => R and said this is equivalent to (P=>R) ^ (Q=>R). Then just looking at P=>R I arrived at a contradiction, so because F^T if F, the entire initial proposition is false. Where am I going wrong..?
 

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  • #2
Interesting... [itex](P \lor Q) \rightarrow R[/itex]
What is the truth table for this? That is one way of showing it. Namely, what is the value of R for various values of P and Q.

Similarly, what are those values in the case of [itex](P \rightarrow R) \wedge (Q \rightarrow R)[/itex]

Hint: Wolfram Alpha is amazing for checking your truth tables...
 
  • #3
UNChaneul said:
Interesting... [itex](P \lor Q) \rightarrow R[/itex]
What is the truth table for this? That is one way of showing it. Namely, what is the value of R for various values of P and Q.

Similarly, what are those values in the case of [itex](P \rightarrow R) \wedge (Q \rightarrow R)[/itex]

Hint: Wolfram Alpha is amazing for checking your truth tables...

No that's not my question...I know that this part of my proof is right. It is page 35 of my book lol. My question is that something else must be wrong with my proof
 
  • #4
Your result is correct. The statement you are trying to prove is obviously false for x = 3. I should also add that it does not seem to make much sense in the first place: it starts for "all x", but there are exactly two values of x for which it could possibly be non-trivial. Are you sure you wrote it down properly?
 
  • #5
It is very hard to read what you have written- it surely would have been less trouble just to type the problem here! It appears to ask you to prove "if x^2= 12- x then either x= -1 or (x+ 3)/(x+1) is greater than or equal to 12".

The only thing wrong is just what you say- this is NOT true. If x^2= 12- x then x is either 3 or -4. Neither of those is -1 so the "x= -1" part is false. If x= 3 then (x+3)/(x+ 1) is (3+3)(3+ 1)= 6/4= 3/2 which is NOT "greater than or equal to 12". If x= -4 then (x+ 3)/(x+ 1) is (-4+ 3)/(-4+1)= -1/(-3)= 1/3 which also is OT "greater than or equal to 12".

Check to see if you haven't copied the problem incorrectly.
 
  • #6
the professor wrote it wrong i found out today, but thanks anyways!
 

Related to Bridge to abstract math: what is wrong with following proof

1. What is the purpose of the "Bridge to abstract math"?

The "Bridge to abstract math" is a concept used to help students transition from concrete, tangible mathematics to more abstract, theoretical mathematics. It aims to bridge the gap between the two and make the transition smoother for students.

2. Why is it important to question the validity of a proof?

Questioning the validity of a proof is crucial in mathematics as it helps to identify any errors or inconsistencies in the logic. This ensures that the proof is accurate and can be relied upon to provide a correct solution to a problem.

3. What are some common mistakes made in proofs?

Common mistakes made in proofs include incorrect assumptions, circular reasoning, and using ambiguous language. These mistakes can lead to an invalid proof and ultimately an incorrect solution to a problem.

4. How can one improve their proof-writing skills?

One can improve their proof-writing skills by practicing regularly, seeking feedback from others, and studying and analyzing well-written proofs. It is also important to have a solid understanding of mathematical concepts and logical reasoning.

5. Is it possible for a proof to be correct but still have flaws?

Yes, it is possible for a proof to be technically correct but still have flaws. This can occur when the proof is valid but does not provide a complete or thorough explanation, or when it relies on faulty assumptions. It is important to thoroughly analyze and critique a proof to ensure its accuracy.

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