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Problem 10 Assume n is an even integer and assume there are n students in class. We want to form as many as possible clubs such that: (a) each club is of even size, and (b) the intersection of every two clubs is also of even size. Prove by Rank-Nullity Theorem that there are at most 2n/2 such clubs.

Problem 10 Assume n is an even integer and assume there are n students in class. We want to form as many as possible clubs such that: (a) each club is of even size, and (b) the intersection of every two clubs is also of even size. Prove by Rank-Nullity Theorem that there are at most 2n/2 such clubs.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 10 Assume n is an even integer and assume there are n students in class. We want to form as many as possible clubs such that: (a) each club is of even size, and (b) the intersection of every two clubs is also of even size. Prove by Rank-Nullity Theorem that there are at most 2″/2 such clubs.
Transcribed Image Text:Problem 10 Assume n is an even integer and assume there are n students in class. We want to form as many as possible clubs such that: (a) each club is of even size, and (b) the intersection of every two clubs is also of even size. Prove by Rank-Nullity Theorem that there are at most 2″/2 such clubs.
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