   Chapter 13.5, Problem 37E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# DISCUSS ■ DISCOVER ■ PROVE ■ WRITEDISCUSS: True or False? Determine whether each statement is true or false. If you think the statement is true, prove it. If you think it is false, give an example in which it fails.(a) p ( n ) = n 2 − n + 11 is prime for all n .(b) n 2 > n for all n ≥ 2 .(c) 2 2 n + 1 + 1 is divisible by 3 for all n ≥ 1 .(d) n 3 ≥ ( n + 1 ) 2 for all n ≥ 2 .(e) n 3 − n is divisible by 3 for all n ≥ 2 .(f) n 3 − 6 n 2 + 11 n is divisible by 6 for all n ≥ 1 .

To determine

(a)

The statement, p(n)=n2n+11 is prime for all n, is true or false and the reason for it.

Explanation

Given:

The expression is,

p(n)=n2n+11

Approach:

Substitute the values of n in the statement.

Calculation:

Substitute 11 for n in the statement p(n)=n2n+11 as follows,

To determine

(b)

The statement n2>n for all n2, is true or false and the reason for it.

To determine

(c)

The statement 22n+1+1 is divisible by 3 for all n1, is true or false and the reason for it.

To determine

(d)

The statement n3(n+1)2 for all n2, is true or false and the reason for it.

To determine

(e)

The statement n3n is divisible by 3 for all n2, is true or false and the reason for it.

To determine

(f)

The statement, n36n2+11n is divisible by 6 for all n1, is true or false and the reason for it.

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