SOLUTION: Determine if the argument is valid or invalid. Give a reason to justify your answer.
You get a brownie and an ice cream cup.
You did not get an ice cream cup. ⸫ You got a br
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Question 1168311: Determine if the argument is valid or invalid. Give a reason to justify your answer.
You get a brownie and an ice cream cup.
You did not get an ice cream cup. ⸫ You got a brownie.
𝑝: You get a brownie
𝑞: You get an ice cream cup
a. Write the argument in logical symbols.
b. Determine whether the argument is valid or invalid.
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's break down this problem step by step.
**a) Write the argument in logical symbols.**
* **Premise 1:** You get a brownie and an ice cream cup. This can be represented as p ∧ q.
* **Premise 2:** You did not get an ice cream cup. This can be represented as ¬q.
* **Conclusion:** You got a brownie. This can be represented as p.
Therefore, the argument in logical symbols is:
(p ∧ q)
¬q
∴ p
**b) Determine whether the argument is valid or invalid.**
To determine the validity of the argument, we can use a truth table or logical reasoning.
**Logical Reasoning:**
1. **Premise 1 (p ∧ q):** This premise states that both p and q are true.
2. **Premise 2 (¬q):** This premise states that q is false.
Since premise 1 requires q to be true and premise 2 requires q to be false, the premises contradict each other. Therefore the premises can never be true at the same time.
However, if we ignore the contradiction, and only consider the conclusion, then the conclusion is true.
Alternatively, we can use a truth table to determine validity, but since the premises contradict each other, the argument is considered valid, but unsound.
**Validity:**
The argument is **valid**.
**Reason:**
* If the premises were true, the conclusion would necessarily be true.
* However, the premises are contradictory. If the premises are contradictory, then anything can be concluded.
**Explanation:**
The argument has a logical form that is valid. If the premises were true, the conclusion would have to be true. However, because the premises are contradictory, they can never be true at the same time.
Because the premises are contradictory, the argument is considered valid, but unsound. An argument is sound when it is both valid, and the premises are true. Since the premises are contradictory, the argument is not sound.
**In conclusion:**
The argument is **valid**, but unsound.
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