Can anyone show me an example of how to do "modus ponens and "modus tollens". I have to write an argument in symbols using sentence letters and truth functional connectives. I have no clue to grasp the concept.
A conditional sentence with a false antecedent is always (Points : 1)
true.
false.
Cannot be determined.
not a sentence.
2. What is the truth value of the sentence "P v ~ P"? (Points : 1)
True
False
Cannot be determined
Not a sentence
3. "Julie and Kurt got married and had a baby" is best symbolized as (Points : 1)
M v B
M & B
M ¡æ B
M ¡ê B
4. If P is false, and Q is false, the truth-value of "P ¡êQ" is (Points : 1)
false.
true.
Cannot be determined.
All of the above.
5. Truth tables can (Points : 1)
display all the possible truth values involved with a set of sentences.
determine what scientific claims are true.
determine if inductive arguments are strong.
determine if inductive arguments are weak.
6. The sentence "P ¡ê Q" is best read as
(Points : 1)
If P then Q
If Q then P
P or Q
P if and only if Q
7. A sentence is said to be truth-functional if and only if (Points : 1)
the sentence might be true.
the truth-value of the sentence cannot be determined from the truth values of its components.
the truth-value of the sentence is determined always to be false.
the truth-value of the sentence can be determined from the truth values of its components.
8. If P is true, and Q is false, the truth-value of "P v Q" is (Points : 1)
false.
true.
Cannot be determined
All of the above
9. The sentence "P ¡æ Q" is read as (Points : 1)
P or Q
P and Q
If P then Q
Q if and only P
10. "P v Q" is best interpreted as (Points : 1)
P or Q but not both P and Q
P or Q or both P and Q
Not both P or Q
P if and only if Q
No getting the right anwsers.
Sure! I can help you understand and create an example of both "modus ponens" and "modus tollens" using symbols and truth functional connectives.
First, let's define what "modus ponens" and "modus tollens" are:
1. Modus Ponens:
Modus ponens is a valid logical inference that states if we have a conditional statement (p → q), and we know that the antecedent (p) is true, then we can assert that the consequent (q) must also be true.
2. Modus Tollens:
Modus tollens is another valid logical inference that states if we have a conditional statement (p → q), and we know that the consequent (q) is false, then we can conclude that the antecedent (p) must also be false.
Now, let's create an argument using both of these inference rules:
Statement 1: If it is raining (p), then the ground is wet (q). (p → q)
Statement 2: It is raining (p).
Using modus ponens, we can conclude that the ground is wet (q) based on the two statements above.
Argument 1:
Premise 1: (p → q)
Premise 2: p
Conclusion: q
This argument follows the "modus ponens" pattern because the premises include a conditional statement and the antecedent of that conditional statement, allowing us to validly conclude the consequent.
Now, let's create an argument using modus tollens:
Statement 3: If it is daytime (r), then it is not dark outside (s). (r → ¬s)
Statement 4: It is dark outside (s).
Using modus tollens, we can conclude that it is not daytime (r) based on the two statements above.
Argument 2:
Premise 1: (r → ¬s)
Premise 2: s
Conclusion: ¬r
This argument follows the "modus tollens" pattern because the premises include a conditional statement and the negation of its consequent, allowing us to validly conclude the negation of the antecedent.
Remember, when using symbols and truth functional connectives, you can represent "if-then" statements using the material implication symbol (→) and negation using the negation symbol (¬). Assign sentence letters to represent the propositions involved and apply the respective inference rule.
I hope this example helps you grasp the concept of "modus ponens" and "modus tollens"! If you have any more questions, feel free to ask.