Given the set of premises, identify the conclusion that creates a valid syllogism. Using an Euler diagram is
recommended.
All postpositivists believe in one reality. Some postpositivists conduct mixed method research.
What is the valid conclusion?
No one who believes in one reality conducts mixed method research.
Some people who believe in one reality conduct mixed method research.
All people who believe in one reality conduct mixed method research.
All people who conduct mixed method research believe in one reality.

Question

UpStudy AI · Accepted Answer

1. Represent the premises using sets:
   - Let $$ P $$ be the set of all postpositivists.
   - Let $$ R $$ be the set of all people who believe in one reality.
   - Let $$ M $$ be the set of all people who conduct mixed method research.

2. The first premise, "All postpositivists believe in one reality", can be written as:
   $$
   P \subset R.
   $$

3. The second premise, "Some postpositivists conduct mixed method research", indicates that:
   $$
   P \cap M \neq \emptyset.
   $$

4. Since $$ P \subset R $$, any element in $$ P $$ is also in $$ R $$. Given that $$ P \cap M \neq \emptyset $$, there exists at least one element that is in both $$ P $$ and $$ M $$; this element is also in $$ R $$.

5. Therefore, there exists at least one element in the intersection of $$ R $$ and $$ M $$:
   $$
   R \cap M \neq \emptyset.
   $$
   This means "Some people who believe in one reality conduct mixed method research."

Thus, the valid conclusion is:

$$ \text{Some people who believe in one reality conduct mixed method research.} $$
Some people who believe in one reality conduct mixed method research.

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