p → ¬p, p ,r→ q `¬r is valid or invali
The given statement "p → ¬p, p, r→ q, ¬r" is invalid.
To prove this, we can use a truth table. Let's break down the statement:
1) p → ¬p: In a truth table, when p is true, ¬p is false. This means that p → ¬p is false when p is true.
2) p: This statement simply says that p is true. Let's say that p is true.
3) r → q: To evaluate this statement, we need to know the truth values of r and q. However, they are not given. So, we cannot determine the validity of this statement based on the given information.
4) ¬r: This statement says that r is false. Let's say that ¬r is true.
Now, let's construct a truth table with the above information:
| p | ¬p | r | q | ¬r | p → ¬p | r → q |
|---|----|---|---|----|--------|-------|
| T | F | F | ? | T | F | ? |
Since we have a question mark for the truth value of r → q, we cannot determine whether the statement as a whole is valid or invalid.
p → ¬p, p ,r→ q `¬r is valid or invali
Apologies for the confusion in my previous response. Let's reassess the given statement:
The given statement is: "p → ¬p, p, r → q, ¬r".
1) p → ¬p: The statement "p → ¬p" is always false. This is known as a contradiction because it states that if p is true, then ¬p must be true, which is impossible.
2) p: This statement says that p is true.
3) r → q: We don't have any information about the truth values of r and q, so we cannot determine the validity of this statement.
4) ¬r: This statement says that r is false.
Now let's construct a truth table with the given information:
| p | ¬p | r | q | ¬r | p → ¬p |
|---|----|---|---|----|--------|
| T | F | ? | ? | T | F |
Since we have question marks for the truth values of r, q, and ¬q, we cannot determine whether the statement as a whole is valid or invalid.
To determine whether the argument "p → ¬p, p, r → q, ¬r" is valid or invalid, we can use the rules of propositional logic to evaluate each step.
Step 1: Given p → ¬p – This statement is an example of a contradiction. According to the Law of Non-Contradiction, a statement and its negation cannot both be true. Therefore, this premise is false.
Since the first premise is false, we can conclude that the argument is invalid.