Question

Using Venn diagrams, test the following syllogistic forms for validity: 1. All $M$ is $P$. All $M$ is $S$. $\therefore$ All $S$ is $P$. 2. All $P$ is $M$. All $M$ is $S$. $\therefore$ All $S$ is $P$. 3. All $M$ is $P$. Some $M$ is $S$. $\therefore$ Some $S$ is $P$. 4. All $P$ is $M$. Some $M$ is $S$. $\therefore$ Some $S$ is $P$. 5. All $P$ is $M$. $\therefore$ Some $S$ is $M$. 6. All $P$ is $M$ Some $S$ is not $M$. $\therefore$ Some $S$ is not $P$. 7. All $M$ is $P$. Some $S$ is not $M$. $\therefore$ Some $S$ is not $P$. 8. All $M$ is $P$. Some $M$ is not $S$. $\therefore$ Some $S$ is not $P$. 9. No $M$ is $P$. Some $S$ is $M$. $\therefore$ Some $S$ is not $P$. 10. No $P$ is $M$. Some $S$ is $M$. $\therefore$ Some $S$ is not $P$. 11. No $P$ is $M$. Some $S$ is not $M$. $\therefore$ Some $S$ is not $P$. 12. No $M$ is $P$. Some $S$ is not $M$. $\therefore$ Some $S$ is not $P$ 13. No $P$ is $M$. Some $M$ is not $S$. $\therefore$ Some $S$ is not $P$. 14. No $P$ is $M$. No $M$ is $S$. $\therefore$ No $S$ is $P$. 15. No $P$ is $M$ All $M$ is $S$. $\therefore$ No $S$ is $P$. 16. No $P$ is $M$. All $S$ is $M$. $\therefore$ No $S$ is $P$. 17. All $P$ is $M$. No $S$ is $M$. $\therefore$ No $S$ is $P$. 18. All $M$ is $P$. No $S$ is $M$. $\therefore$ No $S$ is $P$. 19. Some $M$ is $P$. Some $M$ is not $S$. $\therefore$ Some $S$ is not $P$. 20. Some $P$ is $M$. Some $S$ is not $M$. $\therefore$ Some $S$ is $P$. 

   Using Venn diagrams, test the following syllogistic forms for validity:
1. All $M$ is $P$. All $M$ is $S$.
$\therefore$ All $S$ is $P$.
2. All $P$ is $M$. All $M$ is $S$.
$\therefore$ All $S$ is $P$.
3. All $M$ is $P$.

Some $M$ is $S$.
$\therefore$ Some $S$ is $P$.
4. All $P$ is $M$.

Some $M$ is $S$.
$\therefore$ Some $S$ is $P$.
5. All $P$ is $M$.
$\therefore$ Some $S$ is $M$.
6. All $P$ is $M$

Some $S$ is not $M$.
$\therefore$ Some $S$ is not $P$.
7. All $M$ is $P$. Some $S$ is not $M$.
$\therefore$ Some $S$ is not $P$.
8. All $M$ is $P$. Some $M$ is not $S$.
$\therefore$ Some $S$ is not $P$.
9. No $M$ is $P$. Some $S$ is $M$.
$\therefore$ Some $S$ is not $P$.
10. No $P$ is $M$. Some $S$ is $M$.
$\therefore$ Some $S$ is not $P$.
11. No $P$ is $M$. Some $S$ is not $M$.
$\therefore$ Some $S$ is not $P$.
12. No $M$ is $P$. Some $S$ is not $M$.
$\therefore$ Some $S$ is not $P$
13. No $P$ is $M$. Some $M$ is not $S$.
$\therefore$ Some $S$ is not $P$.
14. No $P$ is $M$. No $M$ is $S$.
$\therefore$ No $S$ is $P$.
15. No $P$ is $M$ All $M$ is $S$.
$\therefore$ No $S$ is $P$.
16. No $P$ is $M$. All $S$ is $M$.
$\therefore$ No $S$ is $P$.
17. All $P$ is $M$.
No $S$ is $M$.
$\therefore$ No $S$ is $P$.
18. All $M$ is $P$.
No $S$ is $M$.
$\therefore$ No $S$ is $P$.
19. Some $M$ is $P$. Some $M$ is not $S$.
$\therefore$ Some $S$ is not $P$.
20. Some $P$ is $M$.
Some $S$ is not $M$.
$\therefore$ Some $S$ is $P$.
Show more…
Cengage Advantage Books: Understanding Arguments: An Introduction to Informal Logic
Cengage Advantage Books: Understanding Arguments: An Introduction to Informal Logic
Walter… 9th Edition
Chapter 7, Problem 7 ↓

Instant Answer

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Step 1

Step 2: Draw Venn diagrams for the premises. Use three circles to represent the sets: $M$, $P$, and $S$. Step 3: Shade areas that are not included in the premises. For example, if a premise states "All $M$ is $P$", shade the area outside of $P$ that overlaps  Show more…

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Using Venn diagrams, test the following syllogistic forms for validity: 1. All $M$ is $P$. All $M$ is $S$. $\therefore$ All $S$ is $P$. 2. All $P$ is $M$. All $M$ is $S$. $\therefore$ All $S$ is $P$. 3. All $M$ is $P$. Some $M$ is $S$. $\therefore$ Some $S$ is $P$. 4. All $P$ is $M$. Some $M$ is $S$. $\therefore$ Some $S$ is $P$. 5. All $P$ is $M$. $\therefore$ Some $S$ is $M$. 6. All $P$ is $M$ Some $S$ is not $M$. $\therefore$ Some $S$ is not $P$. 7. All $M$ is $P$. Some $S$ is not $M$. $\therefore$ Some $S$ is not $P$. 8. All $M$ is $P$. Some $M$ is not $S$. $\therefore$ Some $S$ is not $P$. 9. No $M$ is $P$. Some $S$ is $M$. $\therefore$ Some $S$ is not $P$. 10. No $P$ is $M$. Some $S$ is $M$. $\therefore$ Some $S$ is not $P$. 11. No $P$ is $M$. Some $S$ is not $M$. $\therefore$ Some $S$ is not $P$. 12. No $M$ is $P$. Some $S$ is not $M$. $\therefore$ Some $S$ is not $P$ 13. No $P$ is $M$. Some $M$ is not $S$. $\therefore$ Some $S$ is not $P$. 14. No $P$ is $M$. No $M$ is $S$. $\therefore$ No $S$ is $P$. 15. No $P$ is $M$ All $M$ is $S$. $\therefore$ No $S$ is $P$. 16. No $P$ is $M$. All $S$ is $M$. $\therefore$ No $S$ is $P$. 17. All $P$ is $M$. No $S$ is $M$. $\therefore$ No $S$ is $P$. 18. All $M$ is $P$. No $S$ is $M$. $\therefore$ No $S$ is $P$. 19. Some $M$ is $P$. Some $M$ is not $S$. $\therefore$ Some $S$ is not $P$. 20. Some $P$ is $M$. Some $S$ is not $M$. $\therefore$ Some $S$ is $P$.
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