Poetic Logic
Roses are red ; Violets are blue . The whole poem’s false If line 3 is true.
In the poem above You might get confused. At most how many lines Can be labeled as true?
This is my (first) entry to the Math Poetry Contest .
Assumptions : Line 4 is the entire conditional statement, not just half. "The whole poem" means every line in the poem. You do not have any prior knowledge about the color of flowers.
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4 solutions
What about line 4
Line 4, as indicated in the "Assumptions" note, is the conditional statement, so it can essentially be ignored. Also, an "if" statement can't really be true or false anyway.
You will not find any roses which are not of any color other than r d and you will not find any violets which are not of any color other than b l u e . So, every line in the poem is true except the third one as it says that the above two statements are false but they are actually true.
∴ A total of 3 statements are true in the poem.
The first sentence isn't necessarily true. However, the rest of the solution is correct.
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Why ??? Roses are not red
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As in most logic problems, outside knowledge isn't supposed to exist. For all you know, in the universe this problem exists in, roses could be blue. I added an assumption earlier stating "Assume you don't have any prior knowledge about flower colors."
Line 1,2,4 are true and line3 is false
Ok, by why?
R o s e s a r e r e d ,
B u t v i o l e t s n o t b l u e ,
W h i c h d o e s n ′ t m a k e t h i s p o e m t r u e ,
L i n e 3 n o w i s s a t i s f i e d ,
a n d t h e n a l s o l i n e 4 r i g h t ,
I f w e n o w c o u n t c a r e f u l l y
W e e n d u p w i t h t h e n u m b e r 3
This is the right answer, but the method isn't correct. If the whole poem is false, that means Line 3 is now false and true at the same time, leading to a paradox. Also, violets can be blue.
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Want to ask, how is it 3? Line 3 is false, as you explained. Following that 3 is the correct answer, Line 4 is true. I feel that what Line 4 is saying is a combination of Line 3 and 4. So if Line 3 is false and Line 4 is true, then the condition is satisfied but the prediction isn’t. So Line 4 is false. Is it a pradox or am I wrong?
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Yes, this is known as Curry's paradox . I wrestled with this problem for an hour deciding whether the answer would be 2 or 3. However, I realized that, since Line 3 is false, that means Line 4 doesn't have any definite truth value. Therefore, I figured that we could label lines 1, 2, and 4 as true.
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@Blan Morrison – That’s a good explanation. :) Thanks! But wait, can you just not label Line 4?
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@Jerome Te – No problem! If you want more little challenges like this, I was inspired by the Truth Tellers and Liars practice quizzes.
@Jerome Te – In Formal Logic, all statements must have a value of either true or false.
Also, the question asks for the maximum amount of true statements.
Oh, I understood line 3 as being true if at least one line of the poem is false. So, if I understand you correctly, lines 1, 2 and 4 are true, right?
There was an assumption about having no knowledge of flower colours.
Line 3, "This whole poem is false", can either be true or false.
If it is true , then the whole poem must be false. But since "the whole poem" includes line 3 itself, this would be a contradiction (line 3 would be both true and false).
If it is false , then the whole poem does not need to be false, and the remaining 3 lines can all be true.