Question

i dont know how to do this . How can i apply that table to my question?

Answer 1

My textbooks example

Answer 2

@Hero

Answer 3

So what is your question concerning this? Seems straightforward to me.

Answer 4

Basically, instead of using values of \(n\) you have to use values of \(a\) and \(b\) to disprove the statement.

Answer 5

hmm, i think the table is easier to do but do you know how i can create the table from that example?

Answer 6

Check it:

$$\displaystyle \begin{array}{|c|c|c|c|c|}
\hline
a & b & 5\ \mathrm{divides} \ a & \ 5\ \mathrm{divides} \ b & 5\ \mathrm{divides} \ ( 5a\ +\ b)\\
\hline
1 & 1 & \mathrm{no} & \mathrm{no} & \mathrm{no}\\
\hline
2 & 1 & \mathrm{no} & \mathrm{no} & \mathrm{no}\\
\hline
3 & 1 & \mathrm{no} & \mathrm{no} & \mathrm{no}\\
\hline
4 & 1 & \mathrm{no} & \mathrm{no} & \mathrm{no}\\
\hline
5 & 1 & \mathrm{yes} & \mathrm{no} & \mathrm{no}\\
\hline
\end{array}$$

Answer 7

Created using Mathcha

Answer 8

The last row proves it to be false

Answer 9

dang lol, how come a has all " 1's"?

Answer 10

You mean b has all ones.

Answer 11

b*

Answer 12

Because we need to test one case at a time. We're only testing for different values of a to see what happens. a is the variable, b is like the control.

Answer 13

Anyways you have what you need I think

Answer 14

Very easy to create tables in mathcha

Answer 15

hmm the 3rd and 4th column is out hypothesis?

Answer 16

I don't understand your question. What do you mean by "out hypothesis"?

Answer 17

i mean our*. sorry i am on mobile .. i tend to create typos

Answer 18

Basically if 5 divides a OR if 5 divides b is the hypothesis, then 5 divides (5a + b) is the conclusion. But the conclusion is false

Answer 19

isnt the hypothesis more like the truth table?
where i highlighted

Answer 20

we end up getting T V F= T?

Answer 21

If you want to write it up like a truth table, by all means. Go for it.

Answer 22

It won't change the conclusion

Answer 23

in this case, how would you create a truth table for it ?

Answer 24

Change the no's to F and the yes to T

Answer 25

But the conclusion will still be false because we want T V F conclusion T if the original statement is true, but it is false, therefore we get T V F conclusion F which proves the original statement to be false.

Answer 26

i see, that makes sense. What if we had an extra variable like C for the table. Would c be 1 as well?

Answer 27

Just depends on what proof you're working with.

Answer 28

oh okay, got it. I 'll work on some more problems . :)

Answer 29

Good luck