Question

give a counterexample of the following conjecture.
if a,b,c, and, d are real numbers such that a>b and c>d , then ac > bd.

Answer 1

Let a=-2 and b=-1 such that -2<-1
Let c=-1 and d=4 such that -1<10
Then (-2)(-1)>(-1)(4)

Answer 2

Kinda confusing but just go over the numbers

Answer 3

@rxinstorm Do you follow?

Answer 4

not really...i suck at math, sorry.

Answer 5

Ok do you follow the statement
if a,b,c, and, d are real numbers such that a>b and c>d , then ac > bd.

Answer 6

where did you get those numbers from though? blacklabel

Answer 7

^

Answer 8

Guys dont show your ignorance -.-
Counter examples are examples that show that a statement is false. You can pull any number out of the bag as long as you show that its not true

Answer 9

I'm just wondering, maybe that's what she needs to learn?

Answer 10

She needs to learn what the original statement means.
if a,b,c, and, d are real numbers such that a>b and c>d , then ac > bd
This means lets say there are 4 different number a,b,c and d
and numbers a and c are smaller than numbers b and d
thennn they are assuming that when you multiply the 2 smaller number it will be a smaller number than when you multiply the 2 bigger numbers

Answer 11

umm what grade are you in?

Answer 12

me? 10th.

Answer 13

ohhhhh weird that u gotta do this kind of math

Answer 14

why do you say that

Answer 15

this isnt smth I covered in HS
I think its doable but I just feel that you are lacking basic knowledge to even solve this problem

Answer 16

im in geometry. its actually in a review packet that im doing. i have midterms tomorrow......

Answer 17

I can attempt to explain but Its not something you learn on one foot

Answer 18

Umm you understand that a,b,c and d are variables that can assume any value right

Answer 19

true. but it actually kind of made sense to me, when you were explaining it earlier.

Answer 20

yes

Answer 21

Ok a conjecture is a statement that has been made after much thought but not neccesarily is it true

Answer 22

For example I think that your hair is black . Its a statement that I have made but its not necessarily true

Answer 23

oohhh

Answer 24

A counter example is taking an example and showing that whtvr i said isnt true
SO for example you would get on cam and show that your hair is blonde. Basically you can take any example and show how the statement isnt true

Answer 25

alright, i got it. but like, how do i write down the answer for this question?

Answer 26

So basically the conjecture or the statement that was proposed is
if a,b,c, and, d are real numbers such that a>b and c>d , then ac > bd

Answer 27

We have to show that this aint true

Answer 28

Ok so you give me examples of a, b c and d
and make sure that a equals less than b
and that c equals less than d

Answer 29

should i use numbers?

Answer 30

and then we will multiply the 2 smaller numbers and the 2 bigger numbers and see if a*c<b*d

Answer 31

Yess of course. These dummy variables just mean that you can choose any number that fits the conditions

Answer 32

lol ok

Answer 33

-1 < 2 and 1 < 3
a= -1, b=2, c=1, d= 3.
therefore ac < bd

Answer 34

is that right....?

Answer 35

Ok good that shows you that the statement is correct.
Now we want to find numbers that shows that the statement IS NOT correct

Answer 36

Which should be just one number that throws it off right?

Answer 37

wait. didnt i just do the one that shows that the statement is not correct?

Answer 38

i just changed the signs. like put < instead of >

Answer 39

._.

Answer 40

Okkkk lets rewrite the question

Answer 41

lol sorry...

Answer 42

fineee sooooo
Let a>b and c>d
Your answer will still be the same
Just switch around your variables

Answer 43

We Just screwed up the variables.... Use your example and just tweak it

Answer 44

a= 2, b= -1, c=3, d= 1. <--- changed it.
now, 2> -1 and 3> 1
meaning, a> b and c> d
the statement is true.

Answer 45

YAAAA :D

Answer 46

yayayay

Answer 47

Okkk now lets find example where the statement isnt true. This is called a counterexample

Answer 48

Its kinda trickyy
Keep in mind that multiplying 2 negative variables will give you a positive value and multiplying a negative with a positive will give you a negative value
You can look at my example that I gave originally. Just remember to switch the variables cuz i screwed up

Answer 49

ok but do i use the same numbers and variables and just change the sign? change ">" to "<" sorry, my laptop died...

Answer 50

Hmmm try it out on your own
Just make sure that a>b and that c>d

Answer 51

ummm and know that -1>-2

Answer 52

ohh ok.
2>3 and 4>5
a=2, b=3, c=4, and d=5

Answer 53

@BlackLabel

Answer 54

Sorry I had to go out for a few minutes

Answer 55

ummm how is 2>3 That cant be????
3>2

Answer 56

2 can NOT be greater than 3

Answer 57

Th original conditions a>b and c>d must be true BUTTTT ac>bd should be false meaning
We want to find numbers such that
a>b and c>d and ac<bd

Answer 58

wait wait

Answer 59

ok but i made a completely false statement on purpose bc we're proving it to be false.

Answer 60

Nope i forgot that you never took a logic course and that you are only in grade 10 -.-
But we want to find values such that the first part is true a>b and c>d BUTTT ac<bd
We only want the second part to be false

Answer 61

Lemme give you a concrete example

Answer 62

If it is raining then it is warm outside
If this statement is false then We need to find a time that it is raining BUT it is cold outside

Answer 63

sigh.

Answer 64

So the first part always stays trueee But the second half is false

Answer 65

See you are missing the basics in order to solve this and thats why I was surprised you were in grade wo

Answer 66

10*

Answer 67

ok so like, 2>1 and 3>5?

Answer 68

Ill give you the answer and you try to understand it ok?

Answer 69

alright.

Answer 70

maybe that will be easier

Answer 71

Ok let a=-2 and b=-3 sooo -2>-3
Let c=1and d=-1 such that 1>-1
Nowwww
ac<bd ----> (-2)(1)<(-3)(-1) ------> -2<3

Answer 72

oh. isnt that what i did earlier?

Answer 73

Ummm Nooo you didnt include the negatives

Answer 74

counterexample is an example that disproves an example.
doesn't matter what numbers you use.
therefore BlackLabel was right about the loophole in your problem about the negatives...
problem said to give counterexample, BlackLabel gave it. Done.