Prove that for every integer n where n is greater than or equal to 2, P (n,n) = P(n, n − 1). • Use the direct proof method. • Explicitly write the universal conditional to expose the hypothesis. • Use the factorial definition of a permutation in your proof. • Give your proof line-by-line, with each line a statement with its justification. You can use the Canvas math editor or write your math statements in English. For example, the universal statement that is to be proved was written in the Canvas math editor. In English it would be: For all integers n greater than or equal to 2, the permutation of n elements taken n at a time equals the permutation of n elements taken n-1 at a time.
Prove that for every integer n where n is greater than or equal to 2, P (n,n) = P(n, n − 1). • Use the direct proof method. • Explicitly write the universal conditional to expose the hypothesis. • Use the factorial definition of a permutation in your proof. • Give your proof line-by-line, with each line a statement with its justification. You can use the Canvas math editor or write your math statements in English. For example, the universal statement that is to be proved was written in the Canvas math editor. In English it would be: For all integers n greater than or equal to 2, the permutation of n elements taken n at a time equals the permutation of n elements taken n-1 at a time.
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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I have the entire proof already. I am mostly working on the justifications for each statement. Please do those, thanks!
Transcribed Image Text:Prove that for every integer n where n is greater than or equal to 2, P (n, n) = P (n, n − 1).
• Use the direct proof method.
• Explicitly write the universal conditional to expose the hypothesis.
Use the factorial definition of a permutation in your proof.
Give your proof line-by-line, with each line a statement with its justification.
You can use the Canvas math editor or write your math statements in English. For example, the universal statement that is to be proved was written in the Canvas math
editor. In English it would be:
For all integers n greater than or equal to 2, the permutation of n elements taken n at a time equals the permutation of n elements taken n-1 at a time.
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