Possible explanation for a question

Hello, I solved a little question in the "Joy of Problem Solving" course and I want to share with you another possible explanation for this question:

Suppose that the local is a knave, so his answer "Yes." means no (he is a knave so he's a liar). Therefore, the statement "If you are a liar , then 1+1 = 2" should be false (if he's really a knave). The statement will only be false only if the hypothesis is true ("If you are a liar") and the conclusion is false ("1+1 =2"). This statement can't be false because the conclusion is true (1+1 really equals to 2). That means that this case is not possible and the man is not a knave, but a knight.

Do you think this is a better explanation?

#Logic

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Good point. I've updated the solution to reflect this. Thank you for your input.

Brilliant Mathematics Staff - 11 months ago

There seems to be extra space in the quotation rows

Mahdi Raza - 10 months, 4 weeks ago

Hi Mahdi, I can't seem to find the extra space that you're referencing.

Brilliant Mathematics Staff - 10 months, 4 weeks ago

@Brilliant Mathematics –

Mahdi Raza - 10 months, 4 weeks ago

@Mahdi Raza – Here you go, under the first and the second quotes, each has an extra empty line. Not much of a big deal though!

Mahdi Raza - 10 months, 4 weeks ago

@Mahdi Raza – Wow, good eye! Thank you, let me file a bug report.

Brilliant Mathematics Staff - 10 months, 4 weeks ago

@Brilliant Mathematics – No worries, that is not a big deal at all! Most people wouldn't even notice, but it just feels great when everything controllable is perfect :)

Mahdi Raza - 10 months, 4 weeks ago

@Mahdi Raza – Keep up the good work Mahdi!

Brilliant Mathematics Staff - 10 months, 4 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$