Club membership & exclusion – Infer the necessary conclusion: Statements: • All members of the Tennis club are also members of the Badminton club. • No woman plays Badminton. Which option must be true?

Introduction / Context:This question combines a subset relation with an exclusion statement. If Tennis ⊆ Badminton and no woman plays Badminton, then women are excluded from every subset of Badminton, including the Tennis club.

Given Data / Assumptions:

• Tennis ⊆ Badminton.
• No Woman ∈ Badminton.

Concept / Approach:Exclusion propagates downward through subsets: if a group is barred from a superset, it is barred from all its subsets. Therefore the women-exclusion at Badminton level automatically blocks membership in Tennis.

Step-by-Step Solution:Assume for contradiction that some woman is a Tennis member.Because Tennis ⊆ Badminton, she would then be a Badminton player.This contradicts “No woman plays Badminton.” Thus no woman can be a Tennis member.

Verification / Alternative check:A Venn diagram with Tennis circle entirely inside Badminton and with the entire Badminton circle labeled “no women” shows Tennis shares the same exclusion.

Why Other Options Are Wrong:

• “Some women play Tennis” / “Some women are Tennis members”: impossible by the exclusion.
• “No Tennis member plays Badminton”: false; in fact every Tennis member is also a Badminton member.

Common Pitfalls:Confusing “subset” with “disjoint,” or reading the second statement as “no woman is a Badminton club member” in a weaker, non-playing sense (the logic here is about playing/membership as stated).

Final Answer:No woman is a member of the Tennis club.