Is this statement true?

Logic Level 1

$a - b - c ≠ a - (b - c)$ is always true, regardless of the numbers.

True False

4 solutions

Blan Morrison
Oct 14, 2018

Let's assume the statement is false: $a-b-c=a-(b-c)$ $a-b-c=a-b+c$ $-c=c$ $0=2c$ $0=c$ \ Checking our work $a-b-0\not=a-(b-0)$ $a-b\not=a-b$ The statement is false when $c=0$ . $\beta_{\lceil \mid \rceil}$

While you arrived at the right answer, I don't agree with your reasoning. You've shown that $\text{The statement is false} \Rightarrow 0=c$ .

You haven't shown (although it is true) that $0=c\Rightarrow \text{The statement is false}$ .

For instance, I could make the statement "Not all horses are the same color." You could assume my statement is false (i.e. all horses are the same color) and deduce that Old Pete over there must then be brown. But you could not say "your statement is false if Old Pete is brown."

Jordan Cahn - 2 years, 7 months ago

I simply gave a set of infinite counterexamples, proving the statement was false. Old Pete's fur color is concrete; it cannot be changed. However, due to the phrase, "regardless of the numbers," we know $c$ can be manipulated to equal 0.

Also, plugging in $c=0$ to the original statement reveals that the statement is false. I have updated the solution.

Blan Morrison - 2 years, 7 months ago

Ekene Franklin
Oct 14, 2018

Infact, it holds when $a = b =c$ . The statement is therefore false.

Magnus Käärik
Feb 28, 2019

When a=b=c=0 the statement holds.

Luke Corey
Oct 14, 2018

0 - 0 - 0 = 0 - (0 - 0), therefore this statement is false.

Is this statement true?

4 solutions

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