Question

Which is a counterexample to this conjecture?



The sum of any two consecutive integers is a composite number.



A.
16 + 17 = 33


B.
10 + 11 = 21


C.
6 + 7 = 13


D.


7 + 8 = 15

Answer 1

Find two consecutive integers whose sum is not a composite number.
One of the 4 choices has a sum that is not composite. Which one is it?

Answer 2

i am still confused

Answer 3

Ok, let's go back tot he beginning.
Do you understand the question and the idea of a counterexample?

Answer 4

no

Answer 5

Ok. Here is the concept.

A statement is made. In your case, the statement is "The sum of any two consecutive integers is a composite number."

You are asked to show this statement to be false by showing one example in which it is not true.

Answer 6

no still confused

Answer 7

Let me explain the idea of a counterexample using a simpler statement.

I make the statement "The sum of any two numbers is 4."

How can you prove that statement false by a counterexample?

All you need to do is come up with one single example of a sum of 2 numbers whose sum is not 4. Now you've proven my statement false.

You state: 3 + 2 = 5; 5 is not 4.
This is a counterexample that proved my statement false.

Answer 8

Now you need to know the terms used in the statement of your problem to understand it.
Do you know what a composite number is?

Answer 9

yep ok tht right it is false

Answer 10

You mean my simple example?

Answer 11

yes

Answer 12

Ok. Now for your problem, you need to find one single example that makes the statement false.

Answer 13

First, you need to understand the statement in your problem.
Do you know what a composite number is?

Answer 14

no

Answer 15

Do you know what a prime number is?

Answer 16

yes

Answer 17

compiste number r even

Answer 18

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&docid=_7-GepZTMoLcFM&tbnid=Dw8au41Ov7UmTM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.mathatube.com%2Ftables-charts-composite-num-chart-html.html&ei=DEXQUrGIGtKuyAGyiYDAAw&bvm=bv.59026428,d.aWc&psig=AFQjCNHjCxIaWyBZ4jKCL7ch8NCyw2Vlyw&ust=1389467262616899

Answer 19

15

Answer 20

OK, an integer, 2 or greater is either a prime number or a composite number.
In other words, when dealing with integers, 2 or greater, a number is either prime or composite.

Answer 21

A prime number is an integer greater than one that is divisible only by 1 and itself.
A composite number is an integer greater than one that has at least one factor other than one and itself.

Answer 22

15 is composite because it is divisible by 1, 3, 5, 15
Notice that 15 is not even, but it is still composite,.

Answer 23

ya i no tht

Answer 24

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&docid=_7-GepZTMoLcFM&tbnid=Dw8au41Ov7UmTM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.mathatube.com%2Ftables-charts-prime-comp-num-chart-html.html&ei=gkXQUs3wCabgyQGGr4DwAw&bvm=bv.59026428,d.aWc&psig=AFQjCNHjCxIaWyBZ4jKCL7ch8NCyw2Vlyw&ust=1389467262616899

Answer 25

7 and 8 are consecutive integers. Their sum is 15, but 15 is composite, so that can't disprove the conjecture because it agrees with the conjecture.

Answer 26

Look at all the choices. In each case, you have the sum of 2 consecutive integers.
Is any of the sums not a composite number?
That is the same as asking: Is any of the sums a prime number?

Answer 27

it is c it is a prime number at the end

Answer 28

Exactly.
C shows the sum of two consecutive integers that is not a composite number. That disproves the conjecture.
The answer is C.

Answer 29

ok thank you for all you help

Answer 30

i got more i need help with

Answer 31

You're welcome.