Whats a counterexample?

Question

i know what it is but i dont know how to use it to prove a conjecture wrong.

my teacher used this as an example but i dont get how the number relate to each other.

conjecture: 2 + 5 = 7

counterexample: 10 + (-6) = 4

how do the numbers relate? can you give me another example? THANK YOU!!!!! i have a quiz on wednesday and i dont know what to do!!! thanks soooooo much!

Answer 1

2 + 5 = 7 is not a conjecture. A conjecture is a general statement, and a counterexample is a case where the statement is false.

E.g. conjecture: all primes are odd.

Counterexample: 2 is a prime but 2 is even.

Answer 2

IDk. But I saw your name and ur picture and I LOVE My Chemical Romance! :-D

Answer 3

Your teacher's example is absolutely terrible.  The first answerer has it right -- a counterexample is a specific example that shows that a conjecture is false.

Someone might claim that "all apples are red," but when you show them a green apple they have to give up on their claim.

Answer 4

It depends on what the conjecture is attempting to prove.  This might be best done by saying things, rather than doing math.  So, let's say the conjecture is "Every time you add 2 numbers, you get a result that's larger than those 2 numbers."  And 1st graders across the world are nodding in agreement right now.

The counterexample would be the thing you can show that disproves the conjecture.  Here, you add a negative number, and the result (4) isn't larger than the 2 numbers.