Question

Indirect Proof!

Answer 1

one sec xD need to attach this >.>

Answer 2

there ^_^

Answer 3

well all you have to do is evaluate the expression. you get 9. 9=13 is a contradiction

Answer 4

@wio It's a pretest so I have no idea what to do xD I know the steps for an indirect proof are:
Step 1 Assume the opposite of the conclusion (or prove statement).
Step 2 Reason logically to show the assumption leads to a contradiction of a known fact.

Be sure to explain your whys!
Step 3 Conclude the assumption is false, which in turn proves the conclusion is true.

Answer 5

really I'm confuzled xD

Answer 6

There are many types of indirect proof. this is proof by contradiction.

Answer 7

People keep using this word. I don't know what it means

Answer 8

xD me neither XD

Answer 9

maybe its like if u say, Sara has red shoes, but the contradiction is, Sara's shoes are not blue :P

Answer 10

Proof by contradiction means, you assume that something is false, then you show that no matter what, it is false.

Answer 11

so how do I answer the question? :( I'm so confused now xD

Answer 12

Okay first, let's talk about if-then.
The opposite of an "if A then B" statement is "A and not B" statement.

Answer 13

so the opposite would be if A, then not B?

Answer 14

Our statement is "IF \(x=40\) THEN \(\frac 25 x-7\neq 13\)"
The opposite statement is "\(x=40\) AND \(\frac 25 x-7=13\)

Answer 15

the if-then- becomes -and not-

Answer 16

okay :D your right, thats how u start an indirect proof! :D

Answer 17

The A part is \(x=4\). The B part is \(\frac 25x-7\neq 13\) the NOT B is \(\frac 25 x-7 = 13\)

Answer 18

So now we must show that

"\(x=4\) AND \(\frac 25 x-7 = 13\)" is always false.

Answer 19

okay :D

Answer 20

I think I'm getting it now xD

Answer 21

So use substitution to combine these equations and you get
"\(\frac 25(40)-7=13\)"

Answer 22

yes! :) then do u add? :P

Answer 23

You simplify the left side.

Answer 24

hmm............16 would be the answer :D

Answer 25

You end up with
"16=13"

Answer 26

oh wait! its 9 = 13! :D

Answer 27

ok

Answer 28

because 2/5 * 40 = 16. 16 - 7 = 9 xD

Answer 29

hello? D: @wio

Answer 30

Sure.

Answer 31

so I was right? :)

Answer 32

You were wrong but then made it right.

Answer 33

phew xD so we are done? :)

Answer 34

yeah, well you have to say that \(9=13\) always false. So the original statement if A then B must always true

Answer 35

yes! :D thanks a bunch wio!