What Day is Today?

Logic Level 1

Tom asks Peter what day is today, Peter replied:

"If tomorrow is not Tuesday, then the day after tomorrow is Friday. If the day before yesterday is not Monday, then yesterday is Wednesday."

If he is telling the truth, what day is today?

Monday Thursday Friday Sunday Tuesday Saturday Wednesday

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Kenneth Tan by Kenneth Tan , 21, Malaysia

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1 solution

"If tomorrow is not Tuesday, then the day after tomorrow is Friday" is equivalent to the statement "If today is not Monday, then today is Wednesday". From this we know that the day in question must either be Monday or Wednesday.

"If the day before yesterday is not Monday, then yesterday is Wednesday" is equivalent to the statement "If today is not Wednesday, then today is Thursday". From this we know that the day in question must either be Wednesday or Thursday.

The only day these two statements have in common is Wednesday, and hence is the only potential solution. Since both of the original statements, when reread with this day in mind, are satisfied, we can conclude that the day in question is indeed W e d n e s d a y . \boxed{Wednesday}.

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My approach was exactly the same.

Prasun Kumar - 5 years, 8 months ago

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It's obvious if day after tomorrow is Friday then today is Wednesday!😎 lol..

Anurag Yadav - 5 years, 8 months ago

"If today is not Monday, then today is Wednesday."

"If today is not Wednesday, then today is Thursday."

(Mon OR Wed) AND (Wed OR Thur) = t r u e true is n o t not necessarily implied. Therefore, I don't agree with the answer.

To read his message in a sequence, I think the answer could be Monday or Wednesday else Thursday. Otherwise, we usually follow the very last one, which is T h u r s d a y Thursday .

Answer: I n d e t e r m i n a t e \boxed{Indeterminate}

Lu Chee Ket - 5 years, 6 months ago

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Let p , q , r p,q,r be the statements "Today is ...." "Monday", "Wednesday" or "Thursday", respectively.

Then looking at a truth table, ( p ∨ q ) ∧ ( q ∨ r ) (p \lor q) \land (q \lor r) is equivalent to q q except in the case where q q is false and both p p and r r are true. But this set of circumstances cannot happen, as it is not possible for a given day to be simultaneously both Monday and Thursday. So although you raise a valid concern, I still believe that it safe to conclude that the statement "Today is Wednesday" is true.

Brian Charlesworth - 5 years, 6 months ago

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Why isn't the solution use if-then material conditional logic? (p v q) ^ (q v r) should not have if and then in the sentence. Either is a possible word, for " Either tomorrow is not Tuesday or the day after tomorrow is Friday, and either the day before yesterday is not Monday or yesterday is Wednesday."

Saya Suka - 3 months, 2 weeks ago

I agree that it is safe to take Wednesday as answer in a context interpreted like this. However, in usual conversation, my experience told me that if not 1 then 3 and if not 3 then 4 simply means either 1, 3 or 4 is the answer with no preference. On the other hand, I can also tell that I usually take the last one if I were forced to prefer one of them. In an ambiguous situation like this, a more general conclusion is just an indeterminate, to be strict, I think.

Lu Chee Ket - 5 years, 6 months ago

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