In each of the following questions two statements are given and these…
2023
In each of the following questions two statements are given and these statements are followed by two conclusions numbered (1) and (2). You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.
Statements:
All the actors are girls. All the girls are beautiful.
Conclusions:
All the actors are beautiful.
Some girls are actors.
- A.
Only (1) conclusion follows
- B.
Only (2) conclusion follows
- C.
Either (1) or (2) follows
- D.
Both (1) and (2) follow
Attempted by 8 students.
Show answer & explanation
Correct answer: D
Concept: Two syllogism rules govern this pair of statements. (1) Conversion - a universal affirmative statement "All A are B" always converts validly to the particular statement "Some B is A." (2) Chaining (the AA mood) - two universal affirmatives "All A are B" and "All B are C" combine directly into the further universal "All A are C."
Application: applying both rules to the given statements:
Statement 1 ("All the actors are girls") and Statement 2 ("All the girls are beautiful") chain by rule (2): actors -> girls -> beautiful, giving the universal "All the actors are beautiful" - so conclusion (1) follows.
Statement 1 ("All the actors are girls") converts by rule (1) into "Some girls are actors" - so conclusion (2) follows directly, without needing Statement 2 at all.
Cross-check: conclusion (1) depends on chaining both statements together, while conclusion (2) depends only on converting Statement 1 - two independent derivations using two different rules, so the outcome is not an either/or relationship between them.
Result: since both derivations are valid, both conclusions follow.