Question
Asked Oct 6, 2019
3 views

Define an integer k to be odd if k − 1 is even. Write up a formal proof of the following, using an indirect proof:

Claim: For any natural numbers m and n, if m is odd and n is odd, then m + n is even.

Prove the following:
For any natural number n, if n2 6n is an even number, then n is an even number.
-
You will use Overleaf
to typeset your solutions to the assignment and
then upload the file to
help_outline

Image Transcriptionclose

Prove the following: For any natural number n, if n2 6n is an even number, then n is an even number. - You will use Overleaf to typeset your solutions to the assignment and then upload the file to

fullscreen
check_circle

Expert Answer

Step 1

Consider the following information and prove the following:

for any natural number n, if n' +6n is an even number then n is an even number
help_outline

Image Transcriptionclose

for any natural number n, if n' +6n is an even number then n is an even number

fullscreen
Step 2

Prove the above result by contradiction:

Since, if n2+6n is an even number then n is an even number.

Let’s ...

n26n (2k 1) +6(2k +1)
= 4k2 +1+4k +12k +6
=2(2k 8k +3) +1 where, 2k 8k+3= p, p is any integer
=2p+1
help_outline

Image Transcriptionclose

n26n (2k 1) +6(2k +1) = 4k2 +1+4k +12k +6 =2(2k 8k +3) +1 where, 2k 8k+3= p, p is any integer =2p+1

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Show that the transformation T(x1, x2) = (2x1 − 2x2, 9x1 − 8x2) is invertible, and find a formula fo...

A: Consider the transformation as,

question_answer

Q: Suppose XX is a set with 144 elements that is partitioned into four subsets: X1, X2, X3, and X4. If ...

A: To determine the number of elements in each subset in the partition.

question_answer

Q: Let G be a group. Prove that (ab)1= a"b-1 for all a and b in G if and only if G is abelian

A: First, consider that the group is abelian. So here first compute (ab)-1 for a and b belongs to G, th...

question_answer

Q: 10.

A: Statement: Let G be a group. Prove that the given mapping α (g) = g-1 for all g in G is an auto morp...

question_answer

Q: Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 1111 ​...

A: To find the (integer) values of the variables satisfying the required constraints

question_answer

Q: Refer to the vector space axioms given in class. Determine whether each statement is true or false. ...

A: To find the truth or falsity of the given statements

question_answer

Q: The floor of a room is being covered with tile. An area one fourth14 of the length and one seventh17...

A: Given the length of the floor that have been covered is 1/4th of the area.The width of the room that...

question_answer

Q: Suppose that a sample space has five outcomes {O1,02,03, 04, O5J with corresponding weights w1 1 18W...

A: As per norms, the first three questions are answered. To compute the required probabilities

question_answer

Q: Solve the given differential equation by using an appropriate substitution. The differential equatio...

A: To folve the given Bernoulli type differential equation