Valid and Invalid Logic Arguments: Explained

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In summary: I cannot buy it.If you say, I am rich if and only if I can buy the airport, then if you are not rich, you cannot buy the airport.
  • #1
peos69
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Can anybody help me with the following arguments:

1) If 2+2=5 then 2+3=6 but,2+2=/=5 hence 2+3=/=6

2) If 2+2=4 then 2+3=6 but, 2+2=4 hence 2+3=6

3) if 2+2=5 then 2+3=6 but 2+3=/=6 hence 2+2=/=5

4) if 2+2=4 then 2+3=6 but, 2+3=/=6 hence 2+2=/=4

Which of the above are valid and which are not.

An explanation will help a lot.

Thanks
 
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  • #2
1) Incorrect
2) Correct
3) Correct
4) Correct

You can do these by truth tables (without using Natural deduction) let say you have A and B as two predicates then,

A B A=>B

T T T
T F F
F T T
F F T

Now try ~A and ~B and you should end up with ~B=>~A iff A=>B. In English if you make a statement saying if it rains then it is wet, then if it is dry, it has not rained.

Hope this helps
 
  • #3
Did you learn about truth tables? Can you write down the truth table for A => B and see how that helps you (dis)prove them?

By the way, this is a good exercise. It points out an important mistake made by many people, who start to learn writing down proofs.
 
  • #4
What people do before the truth tables or what other formalistic commodities where discovered? Where in the dark?? MUST ilearn now whatever you call it logic to evaluate those arguments? I KNOW that an argument is valid when the premises of the argument supports the truthfulness of the result,therefor No1 argument is valid
 
  • #5
I am sorry to say that truth tables and natural deduction sounds Chinese to me.
Isnt there another way to evaluate those arguments?
 
  • #6
peos69 said:
What people do before the truth tables or what other formalistic commodities where discovered? Where in the dark?? MUST ilearn now whatever you call it logic to evaluate those arguments? I KNOW that an argument is valid when the premises of the argument supports the truthfulness of the result,therefor No1 argument is valid
No one argument basically says that if it has rained then it is wet, and then it observes that it has not rained. Now you can't say that it is not wet, because rain is not the only thing that causes things to get wet. For truth tables go on http://en.wikipedia.org/wiki/Truth_table . Make sure you look at the examples, they are pretty simple. Some tips,
If A then B is the same as saying A=>B (that is A implies B)
and iff is if and only if which says A=>B and B=>A.

No1 is definitely false, no doubt about it. If you don't understand why, think about it. Rather I should say its not a tautology (which means its not always true).
 
  • #7
Surely if it rains is going to get wet .Those things are interrelated,but the sentences in my examples are not.To oppose your argument i can produce the following argument.
If i am reach i can buy Kennedy Airport,but since i am not reach i cannot buy the said airport
 
  • #8
That's logically false :)
You could get a bank to loan you money and still buy it.
It would be different if you said:
"If and only if (i.e. precisely if, i.e. either both, or neither) I am rich, I can buy Kennedy airport."
Then from "I am not rich" you can draw the conclusion that you can't buy it. But it follows from the "only if" part, not the "If" part.
 
  • #9
Mention The Bank I Will Pay Them A Visit Tomorrow
 
  • #10
And again you did not answerer my question what people did before all those logical commodities were discovered
 
  • #11
I am sorry to say i do not understand
 
  • #12
Implication that is A=>B (If A then B) is true if A is false, regardless of if B is false or not. So if you are not rich then the statement is true regardless if you can buy the airport. The statement would be false if you are rich but you cannot buy the airport.

If you say, I am rich if and only if I can buy the airport, then if you are not rich, you cannot buy the airport.
 
  • #13
.

.[/QUOTE]If you say, I am rich if and only if I can buy the airport, then if you are not rich, you cannot buy the airport.[/QUOTE]

I am sorry i DID NOT say that
 
  • #14
peos69 said:
If i am reach i can buy Kennedy Airport,but since i am not reach i cannot buy the said airport
That is what i said
 
  • #15
It is only true if you say "if and only if" not just "if".
 
  • #16
Would you also agree then that

"If I am rich I can buy a cup of coffee but I am not rich so I cannot buy a cup of coffee"?
 
  • #17
Hallsofivy, i agree...it's all relative!
 
  • #18
A cup of coffee is not the Kennedy Airport
 
  • #19
I am sorry for the mistake in spelling. it is "rich" instead of "reach"
 
  • #20
peos69 said:
A cup of coffee is not the Kennedy Airport
And your point is what? I was under the impression we were talking about airports. Are you now saying that we were only talking about airports?

The discussion at the point where you wrote "If I am rich I can buy the Kennedy Airport" implied "if I am not rich I cannot buy the Kennedy Airport" while everyone had been telling you that "if A then B" does NOT imply "if not A then not B". My point was that your example is not general.
 
  • #21
If you can prove Godels theorems and the consistency of set theory i will jump over the cliff but since you cannot prove them both you saved my life
 
  • #22
And your contention is not general
 
  • #23
NOT everyone ...
 
  • #24
Er, are you feeling well?
 
  • #25
* Wondering if this thread can still be saved?
 
  • #26
SURE perfect after all i am not going to jump over the cliff
 

What is the difference between valid and invalid logic arguments?

A valid logic argument is one where the conclusion logically follows from the premises, meaning that the conclusion must be true if the premises are true. An invalid logic argument is one where the conclusion does not necessarily follow from the premises, making it possible for the conclusion to be false even if the premises are true.

What makes an argument valid or invalid?

An argument is considered valid if the conclusion logically follows from the premises, while an argument is considered invalid if the conclusion does not logically follow from the premises. This means that the conclusion must be supported by the premises in a valid argument, whereas the premises may not adequately support the conclusion in an invalid argument.

Can an invalid argument have a true conclusion?

Yes, an invalid argument can have a true conclusion. The validity of an argument is determined by the logical relationship between the premises and the conclusion, not the truth or falsity of the statements. It is possible for an argument to have a true conclusion even if it is invalid, as long as the conclusion does not logically follow from the premises.

What are some common examples of valid logic arguments?

One common example of a valid logic argument is "If it is raining, the ground is wet. It is raining. Therefore, the ground is wet." This argument follows the logical structure of a modus ponens, where the conclusion is supported by the premises. Other examples include syllogisms, mathematical proofs, and deductive reasoning.

How can I determine if an argument is valid or invalid?

To determine if an argument is valid or invalid, you must assess the logical relationship between the premises and the conclusion. Look for any gaps or flaws in the reasoning and consider whether the conclusion logically follows from the premises. You can also use logical rules and principles to evaluate the validity of an argument.

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