Which are counter examples of the following statement?
If the sum of x and y is negative, then both x and y are negative.

x = -10 and y = 5

x = -2 and y = -4

x = -6 and y = 0

x = 15 and y = -2

Question

Which are counter examples of the following statement?
If the sum of x and y is negative, then both x and y are negative.

 	
	
x = -10 and y = 5
	
x = -2 and y = -4
	
x = -6 and y = 0
	
x = 15 and y = -2

michele_laino · Answer

please what is:
$$15+(-2)=...$$

michele_laino · Answer

hint:
$$15+(-2)=15-2=...$$

directrix · Answer

You are looking for two numbers that add to a negative number BUT one of the numbers added is not negative.

directrix · Answer

Consider this option:

x = 15 and y = -2

 The sum of the two is number is 13 so they do not satisfy the hypothesis of having a negative sum.

So, that option is out.   @theviolentredhead

anonymous · Answer

B @Directrix

directrix · Answer

Not option B, @theviolentredhead 

Because -2 and -4 sum to -6 BUT they are both negative.

We are looking for the sum of two numbers that is negative, but the numbers added to get that sum are not both negative.l

directrix · Answer

So, Options B and D have been ruled out, so far.

directrix · Answer

@theviolentredhead   What is the sum of -10 and 5 ?

mathmath333 · Answer

oh sry option $b$ is in correct

anonymous · Answer

but is says i can have mroe then 1 answers

mathmath333 · Answer

oh now it makes sense

anonymous · Answer

???

directrix · Answer

I know it. If you will just do as I ask, we will finish this problem in a minute and be gone.

We cannot get give you the answer so please help us.

Again, @theviolentredhead    what is the sum of -10 and 5?

(We are testing option A)

anonymous · Answer

so A and B ?

directrix · Answer

what is the sum of -10 and 5?

mathmath333 · Answer

whay is 
$\Huge -10+5$

mathmath333 · Answer

i mean *what is

anonymous · Answer

-5

directrix · Answer

Okay. So this option: x = -10 and y = 5 is correct 

because the two numbers add to a negative but one of them is not negative. 

Option A is correct and there is one more, you said.

directrix · Answer

Option C test:  x = -6 and y = 0

directrix · Answer

What do you get when you add -6 and 0?  What is -6 + 0 = ?   @theviolentredhead

anonymous · Answer

-6

anonymous · Answer

so A B and C are correct

anonymous · Answer

No, only A & C are correct

directrix · Answer

>>>so A B and C are correct   NO

anonymous · Answer

ok thank you

anonymous · Answer

happy new year!!!!!

directrix · Answer

@dazz5   I do not appreciate your interrupting the thread.

Now, tell us why C is correct.

anonymous · Answer

wait A and C are correct?  and not b

anonymous · Answer

???

mathmath333 · Answer

in option 
$b$ the sum of -2 and -4 is negative but both-2 and -4 are negative so 

option b is not correct

anonymous · Answer

Sorry @Directrix  I did not mean to interrupt, I was just trying to help. C is correct because -6 + 0 = -6 (so it evaluates to a negative answer and our individual x and y values are not both negative (i.e.one is positive, the other negative). Therefore it follows the rules of the  counterargument .

anonymous · Answer

This goes for A, as stated above earlier, (-10 + 5= -5) The answer (-5) is negative and the actual x and y values have different signs.

directrix · Answer

@dazz5

No worries.

On this, I wanted to comment:

 -6 + 0 = -6 (so it evaluates to a negative answer and our individual x and y values are not both negative (i.e.one is positive, the other negative). 

Zero is not a positive number. It is neither positive nor negative. Yet, option does qualify as a counterexample because the sum of -6 and 0 is negative and while -6 is negative, zero is not.