#### promitheus

##### New member

- Joined
- Aug 19, 2017

- Messages
- 18

I'm struggling to get my head around this particular example.

Q: Find the error in the following \proof" that 10 = 20. Can you express the incorrect step in terms of an invalid argument?

Suppose that 10 = 20. Then subtracting 15 from both sides we get -5 = 5, and squaring both sides we get (-5)

^{2}= 25 = 5

^{2}, which is true. Therefore our original assumption that 10 = 20 must be true too.

My working/thought process so far:

Let p be the proposition that 10=20

Let q be the manipulations (the subtracting 15 from both sides and squaring)

These are the two premises and the conclusion is that if q, then p (q->p). In order for our conclusion to hold true, both our premises must also be true, and as our proposition p has a truth value of 0, our conclusion cannot be true. Therefore, the argument is invalid.

I'm really unsure of this because the assumption is so obviously wrong, however I'm not sure if my method of proving it is correct?

Would appreciate any feedback.

Cheers.