Respuesta :
Law of Detachment
For the law of detachment to apply, you must have two statements. The first statement must be a conditional statement and the other, a non-conditional but supporting statement. The non-conditional statement must match the hypothesis of the first statement, which is conditional on arriving at a logical conclusion.
The law of detachment gives that:
[tex]\begin{gathered} if\text{ p, then q} \\ \text{then} \\ q\text{ is the conclusion} \end{gathered}[/tex]Law of Syllogism
In the rule of syllogism, there are three parts involved. Each of these parts is called a conditional argument. The hypothesis is the conditional statement that follows after the word if. The inference follows after the word then.
To represent each phrase of the conditional statement, a letter is used. The pattern looks like this:
[tex]\begin{gathered} \text{Statement 1}\Rightarrow\text{ If p, then q} \\ \text{Statement 2}\Rightarrow\text{ If q, then r} \\ Conclusion\Rightarrow\text{ If p, then r} \end{gathered}[/tex]SOLUTION
Let's label the statements as follows:
[tex]\begin{gathered} p=\text{ Terryl completes the course with a grade of C } \\ q=\text{ He will not receive credit} \\ r=\text{ He will have to take the course again} \end{gathered}[/tex]Therefore, the statements are:
[tex]\begin{gathered} \text{if p, then q} \\ \text{if q, then r} \end{gathered}[/tex]Hence, the conclusion is given using the Law of Syllogism:
[tex]if\text{ p, then r}[/tex]The conclusion is "If Terryl completes a course with a grade of C, then he will have to take the course again."
