each question comprises two statements (numbered as I and II) you have to take the statements as true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow from the given statements, disregarding commonly known facts.

(I) some beautiful women are actresses.

(II) All actresses are good dancers

Which of the following derivations is correct?

Correct Answer: Some beautiful women are good dancers.

Step-by-Step Explanation:

Step 1: Analyze the given statements
We are given two statements:
Statement (I): Some beautiful women are actresses.
Statement (II): All actresses are good dancers.

Step 2: Understand the logical structure using Syllogism rules
Let us represent the categories/terms:
- Subject of Statement I: "Beautiful women"
- Middle term: "Actresses"
- Predicate of Statement II: "Good dancers"

Statement (I) tells us that there is an overlap between the set of "beautiful women" and the set of "actresses". In other words, at least some individuals belong to both categories.

Statement (II) tells us that the entire set of "actresses" is completely included within the set of "good dancers".

Step 3: Evaluate the logical derivation/conclusion
Since those "beautiful women" who are "actresses" also belong to the set of "actresses", and every single "actress" is a "good dancer", those specific "beautiful women" must necessarily be "good dancers" as well.

Therefore, we can logically conclude that: "Some beautiful women are good dancers."

Step 4: Check other options
- "All good dancers are actresses": This is incorrect because Statement II says "All actresses are good dancers", which does not imply that all good dancers are actresses (the converse of a universal affirmative statement is not automatically true).
- "Both (a) and (b)": Incorrect since (b) is invalid.
- "None of the above": Incorrect since (a) is valid.

Hence, the correct option/derivation is "Some beautiful women are good dancers."