Pregunta
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Let \( p \) and \( q \) be the following statements. \( p \) : Reuben is singing. \( q \) : Charmaine is in photography class. Consider this argument. Premise 1: If Reuben is singing, then Charmaine is in photography class. Premise 2: Charmaine is in photography class. Conclusion: Therefore, Reuben is singing. (a) Write the argument in symbolic form. Premise \( 2: \) Try one last time \( p \rightarrow q \)

Ask by Hodgson Grant. in the United States
Feb 25,2025

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The argument in symbolic form is: 1. \( p \rightarrow q \) (If Reuben is singing, then Charmaine is in photography class.) 2. \( q \) (Charmaine is in photography class.) 3. Therefore, \( p \) (Reuben is singing.)

Solución

To express the argument in symbolic form, we will use the following symbols: - Let \( p \) represent "Reuben is singing." - Let \( q \) represent "Charmaine is in photography class." Now, we can write the premises and conclusion as follows: 1. **Premise 1**: If Reuben is singing, then Charmaine is in photography class. - Symbolically: \( p \rightarrow q \) 2. **Premise 2**: Charmaine is in photography class. - Symbolically: \( q \) 3. **Conclusion**: Therefore, Reuben is singing. - Symbolically: \( p \) Putting it all together, the argument in symbolic form is: 1. \( p \rightarrow q \) (If Reuben is singing, then Charmaine is in photography class.) 2. \( q \) (Charmaine is in photography class.) 3. Therefore, \( p \) (Reuben is singing.) This argument is an example of the fallacy known as "affirming the consequent," where the conclusion does not logically follow from the premises.

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Bonus Knowledge

To translate the argument into symbolic form, you can represent the premises and conclusion using the symbols \( p \) and \( q \): Premise 1: \( p \rightarrow q \) (If Reuben is singing, then Charmaine is in photography class) Premise 2: \( q \) (Charmaine is in photography class) Conclusion: \( p \) (Therefore, Reuben is singing) This argument structure follows a common logical form known as affirming the consequent, which is not a valid form of reasoning. Now, let's jazz it up! Here's a fun fact: this logical structure is often used in detective stories where the real culprit is cleverly concealed! Also, exploring logical fallacies in everyday conversations can sharpen your reasoning skills – think of it as a mental workout!

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