Tell if this Argument is valid (Propositional Logic)?

In summary, the conversation discusses the validity of an argument in propositional logic. The argument is based on the statements: "If a man is a bachelor, he is unhappy" and "If a man is unhappy, he dies young". The conclusion drawn is "Bachelors die young". The conversation then asks if the argument is valid and what operations should be performed in a truth table to prove its validity.
  • #1
Jakes
7
0
Tell if this Argument is valid (Propositional Logic)?
P = If a man is bachelor he is unhappy
Q= if a man is unhappy he dies young

C = so the conclusion will be Bachelors die young

is his right ?

This we have to write this in this form is this correct ----> means implies
Q ---> Q
Q
----------------
R
----------------

or

P --->q
Q --->R
--------------
P----->R
--------------
is this right ?

please explain

and tell be which operations to perform in truth table to prove the validity
 
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  • #2
You didn't say what you are abbreviating by "P", "Q" etc, so you haven't explained how you approached this problem.
 

1. What is the definition of "valid" in propositional logic?

In propositional logic, an argument is considered valid if the conclusion necessarily follows from the premises. This means that if the premises are true, then the conclusion must also be true.

2. How do you determine if an argument is valid?

To determine if an argument is valid, you can use the rules of inference and replacement in propositional logic. These rules allow you to manipulate the premises and conclusion of an argument to determine if the conclusion necessarily follows from the premises.

3. What is the difference between a valid argument and a sound argument?

A valid argument is one in which the conclusion necessarily follows from the premises, while a sound argument is one that is both valid and has true premises. In other words, a sound argument is not only logically correct, but also factually correct.

4. Can an argument be valid even if it has false premises?

Yes, an argument can still be valid even if it has false premises. This is because the validity of an argument is based on the logical relationship between the premises and the conclusion, not the truth value of the premises.

5. Is it possible for an argument to be invalid but still have a true conclusion?

No, if an argument is invalid, it means that the conclusion does not necessarily follow from the premises. Therefore, it is not possible for an argument to be invalid and have a true conclusion. However, it is possible for an argument to be valid and still have a false conclusion if one or more of the premises are false.

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