Solution Found!
For an integer n, consider the open sentence P(n) : n2 4n + 1 is an odd integer. (a)
Chapter 1, Problem 5(choose chapter or problem)
QUESTION:
For an integer n, consider the open sentence \(P(n): n^{2}-4 n+1\) is an odd integer.
(a) Give an example of an integer n such that P(n) is true.
(b) Give an example of an integer n such that P(n) is false.
Questions & Answers
QUESTION:
For an integer n, consider the open sentence \(P(n): n^{2}-4 n+1\) is an odd integer.
(a) Give an example of an integer n such that P(n) is true.
(b) Give an example of an integer n such that P(n) is false.
ANSWER:Step 1 of 2
(a)
The statement given is \(P(n): n^{2}-4 n+1\), we have to find an integer n such that P(n) is true.
Consider n = 0
\(\begin{aligned} P(n) & : n^{2}-4 n+1=0-4 \times 0+1 \\ & :=1 \end{aligned}\)
As 1 is an odd integer, the statement is true. Thus P(n) is true for n = 0.