Question

question 22

if the first two statements are true, is the final statement true?

all voters are responsible.
most of the people in this room are responsible.

some of the people in this room are voters.

yes
no
uncertain

Explanation:

Analyze the premises

Using the Syllogistic Reasoning knowledge point:

• Premise 1: "All voters are responsible." This means the set of voters is entirely contained within the set of responsible people.
• Premise 2: "Most of the people in this room are responsible." This means a majority subset of the people in this room belongs to the set of responsible people.

Evaluate the conclusion

Using the Venn Diagrams knowledge point:

• We have three sets: Voters (\(V\)), Responsible people (\(R\)), and People in this room (\(P\)).
• We know \(V \subseteq R\).
• We know a large portion of \(P\) is inside \(R\).
• However, there is no specified relationship between \(V\) and \(P\). The voters (\(V\)) and the people in this room (\(P\)) could be completely disjoint (separate), even though both have members inside \(R\).
• Therefore, we cannot guarantee that "Some of the people in this room are voters."

Determine the final truth value

Since the connection between the people in this room and voters is not guaranteed by the premises, the final statement cannot be proven true or false. Thus, the correct option is "uncertain".

Answer:

• yes
• no
• uncertain (Correct answer)