Use mathematical induction to prove the statement is true for all positive integers n.5 + 
+ 
+ . . . + 
= 6
What will be an ideal response?
Answers may vary. Possible answer:
First we show that the statement is true when n = 1.
For n = 1, we get 5 = 6
Since 6
= 6
= 5 , P1 is true and the first condition for the principle of induction is satisfied.
Next, we assume the statement holds for some unspecified natural number k. That is,
Pk: 5 + 
+ 
+ . . . + 
= 6
is assumed true.
On the basis of the assumption that Pk is true, we need to show that Pk+1 is true.
Pk+1: 5 + 
+ 
+ . . . + 
= 6
So we assume that 
is true and add the next term, 
to both sides of the equation.
5 + 
+ 
+ . . . + 
+ 
= 6
+ 
5 + 
+ 
+ . . . + 
+ 
= 6 - 
+ 
5 + 
+ 
+ . . . + 
+ 
= 6 - 
5 + 
+ 
+ . . . + 
+ 
= 6
The last equation says that Pk+1 is true if Pk is assumed to be true. Therefore, by the principle of mathematical induction, the statement 
is true for all natural numbers n.
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A. True B. False
Provide an appropriate response.Determine which of the following is used to solve the inequality 
< c, for c > 0.
A. ax + b < c B. -c < ax + b < c C. ax + b < c or ax + b < -c D. -c < ax + b > c
Use these sets to find the following. Identify any disjoint sets.Let U = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, M = {4, 6, 8, 10}, 
and 
M ? N
A. ?; M and N are disjoint sets. B. {5, 6, 7, 8, 9, 10, 11, 12, 13} C. {4, 5, 6, 7, 8, 9, 13} D. {4, 5, 6, 7, 8, 9, 10, 11, 13}
Simplify.
A. 
B. 
C. 
D. 