Prove that there does not exist a 43 × 30 matrix with entries from {0, 1} such that there are 17 is in each row and in each column.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please solve the two part discrete math question

C. Prove that there does not exist a 43 × 30 matrix with entries from {0, 1} such that there are 17
is in each row and in each column.
D. Let A and B be sets. Prove that (A × B) ^ (B × A) = Ø if and only if ANB = Ø. (Use any
appropriate proof technique.)
Transcribed Image Text:C. Prove that there does not exist a 43 × 30 matrix with entries from {0, 1} such that there are 17 is in each row and in each column. D. Let A and B be sets. Prove that (A × B) ^ (B × A) = Ø if and only if ANB = Ø. (Use any appropriate proof technique.)
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