Using a truth table, check the validity of

thanushasw

thanushasw

Answered question

2022-07-09

Using a truth table, check the validity of the following argument: “If Jane won the competition, then either Mary came second or Silva came third. Silva didn’t come third. Thus, if Mary didn’t come second, then Jane didn’t win the competition.”

Answer & Explanation

Don Sumner

Don Sumner

Skilled2023-05-29Added 184 answers

Let:
- P: Jane won the competition
- Q: Mary came second
- R: Silva came third
The given argument can be broken down into the following logical statements:
Premise 1: If Jane won the competition, then either Mary came second or Silva came third.
Premise 1: P(QR)
Premise 2: Silva didn't come third.
Premise 2: ¬R
Conclusion: If Mary didn't come second, then Jane didn't win the competition.
Conclusion: ¬Q¬P
Now, let's create a truth table to evaluate the validity of the argument:
P Q R P ( Q R ) ¬ Q ¬ P T T T T T T T F T T T F T T T T F F F F F T T T T F T F T T F F T T T F F F T T
In the truth table, we can see that the conclusion is true (T) for all the cases where the premises are true (T). Therefore, the argument is valid based on the truth table analysis.

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