Questions: Draw a Venn diagram for the proposition, and label all regions of the diagram. Based only on the Venn diagram above and the proposition, (not on any other knowledge you have) can you conclude that some dancers are not nurses? Yes, because there are parts of P not in S and parts of S not in P. No, because S and P do not intersect. No, because there are parts of P not in S and parts of S not in P. Yes, because S and P do not intersect. Yes, because S could also contain P. No, because S could also contain P.

Draw a Venn diagram for the proposition, and label all regions of the diagram.
Based only on the Venn diagram above and the proposition, (not on any other knowledge you have) can you conclude that some dancers are not nurses?
Yes, because there are parts of P not in S and parts of S not in P.
No, because S and P do not intersect.
No, because there are parts of P not in S and parts of S not in P.
Yes, because S and P do not intersect.
Yes, because S could also contain P.
No, because S could also contain P.

Transcript text: Draw a Venn diagram for the proposition, and label all regions of the diagram. Based only on the Venn diagram above and the proposition, (not on any other knowledge you have) can you conclude that some dancers are not nurses? Yes, because there are parts of $P$ not in $S$ and parts of $S$ not in $P$. No, because $S$ and $P$ do not intersect. No, because there are parts of $P$ not in $S$ and parts of $S$ not in $P$. Yes, because $S$ and $P$ do not intersect. Yes, because $S$ could also contain $P$. No, because $S$ could also contain $P$.

Solution

Solution Steps

Step 1: Analyze the prompt

The prompt asks to select the Venn diagram that represents the proposition "Some S are not P". It then asks whether we can conclude "some dancers are not nurses," given that _S_ represents dancers and _P_ represents nurses.

Step 2: Select the correct Venn Diagram

The correct Venn diagram is A, which depicts an intersection between S and P, but also a portion of S outside of P. This represents "Some S are P," but also crucially, "Some S are _not_ P."

Step 3: Answer the second question

The correct answer is A. Based _only_ on the diagram and the proposition it represents (some S are not P), we _can_ conclude that some dancers are not nurses. The overlapping portion of the circles shows some dancers are nurses, and the portion of S outside of P shows some dancers are _not_ nurses.

Final Answer

c. A d. A

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