Question

Which of the following is a counter example to the conjecture:
An even number is the sum of two even numbers.
14 = 13 + 1
15 = 5 + 10
11 = 9 + 2
16 = 10 + 6

Answer 1

14 = 13 + 1

Answer 2

thanks love (:

Answer 3

Why is tad1's answer correct? How do we know it's not the others?

Answer 4

yea, tad1 how'd you get that answer?

Answer 5

its the;ast one bc it says two EVEN number's

Answer 6

Bailey -- in the last one you have

EVEN plus EVEN = EVEN

The statement we're looking to DISprove says that all even numbers are the sum of two even numbers. (So it's not the last one)

Answer 7

14 is an even number. The others are odd numbers. the statement said nothing about odd numbers. 16 is also even, but it is the sum of two even numbers. so the counter example has to be 14 = 13 + 1, the sum of two odd numbers equals an eve number which disproves the statement.

Answer 8

then which one is it?,,,im confused

Answer 9

tad1's answer is correct, and he just gave the reason above.
You want to show that (odd + odd) = even.
The equation 13 + 1 = 14 is exactly that.

13 = odd
1 = odd
add them... and you get 14, which is even. :)

Answer 10

thanks ya'll (: