Truth tables or fun with V



Tweedledum and Tweedledee look alike, but Tweedledum lies on Monday, Tuesday, and Wednesday, whereas Tweedledee lies on Thursday, Friday, and Saturday. They both tell the truth on Sunday. You come upon the two of them, and they make the following statements. Determine who is who, and what day it is.

A: Today is Monday or Wednesday.
B: Today is Monday or Sunday.

22 thoughts on “Truth tables or fun with V

  1. I’ll take a shot at this, assuming these dysjunctive statements use the term ‘or’ in the inclusive sense. I’m heading into these truth tables a timid virgin, so wish me luck.

    Wednesday

    A=Dee
    B=Dum

    Both statements cannot be true; therefore it cannot be Sunday. This means that statement B must be false. Statement A cannot also be false, which means A must be true, which means it is either Monday or Wednesday on which Tweedledee tells the truth and Tweedledum lies, which means Tweedledee is A and Tweedledum is B. The true/false conditions apply equally well to Monday or Wednesday; however, because Dum is a lying bastard who tortures people whenever they ask the simplest of questions and he’s stained the good reputation of Monday by uttering his falsehoods, then I shall choose Wednesday if I must choose but a single day.

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  2. I got the same answer -Dee is ‘A’and -Dum is ‘B’ and it is Wednesday. I drew a Monday to Sunday calander for both -Dum and -Dee. then marked which days of the week they coud make statements A or B. That reduced my choices of days of the week to Tuesday, Wednesday and Sunday for -Dum and Monday Wed and Sunday for -Dee. Looking at the two calanders with the possibe choices circled, I had a common day AND opposite letters circled; the answer was staring back at me. The visual aid really helped.

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  3. Yeah, A is Dee and B is Dum. If it is Sunday, then what B says is true and what A says is false; therefore, it is not Sunday. If it is Monday, then what both A and B say are true, so it is not Monday (since the claims of A and B always have opposite truth values, except for Sundays). Therefore, B is lying, and thus A is telling the truth, and thus it is Wednesday, and since Dee tells the truth on Wednesday, A is Dee and B is Dum

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  4. great job, you guys! my head hurts more from reading your answers than it did when I read the question!!

    FYI, ~b, the “v” symbol, or vel, in formal logic does indeed indicate the dysjunct “or”…

    as usual, I have a hard time with these things…I panic first, which only lands me in the uncomfortable position of not knowing where to start with the ciphering, use of truth tables, etc.

    if I met Dee and Dum at the fork in the road, I’d be stuck there, crying, for a long time!!

    even though I know, just as there is no crying in baseball – there is no crying in logic classes!!!!

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  5. Martin’s explanation is concise. Andrew is an empiricist. ~B is lucky.
    Alexandra is 2/3 right.
    I couldn’t figure it out until I read you guys’ stuff.

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  6. Sob, I take exception to your ‘lucky’ term (with holding that Monday also fits the conditions) but point out the source of my ‘lucky’ reasoning: either the entire statement is true or it is false.

    Do we need to pay any mind to the truth value of any false statement’s component parts if one part of the statement is to be judged true while another component is false?

    This was the problem I had with the first example when I couldn’t get both of second statement’s component parts to be false. The correct reasoning seemed (in the first example) to be based on the entire sentence being false, whereas in the second example Roth discards Monday because this one component would seem to be a partial truth in B’s false statement. Remember, the ‘or’ is inclusive. I chose Wednesday because, although B was a false statement in its entirety (regardless whether or not any one component was true), such a choice avoided B’s statement altogether but, as far as I can tell, Monday also fit the conditions. I don’t think my choice was lucky at all; it was reasoned.

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  7. Study the truth tables for “vel” and “aut”:
    With vel the only time the compound is false is when both disjuncts are false; with aut the compound is false when both disjuncts are true and when both are false.

    vel = either…or.. or both
    aut = either ..or..but not both

    1. If φ, ψ are sentences of SL then φ, ψ, (φ —# i/0 are sentences of SLtt.
    2. If φ, ψ are sentences of SLtt then (φ & ψ), (φ v ψ), (φ -• ψ), ~φ are sentences of SL#. (This excludes nested TA’s.)

    as I always say…..

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  8. ~B takes exception. And writes, “Remember, the ‘or’ is inclusive.”

    But, wait. To be inclusive it would have to be true when both disjuncts are true! As Perlo says above how can it be that it is BOTH Monday and Sunday on the same day? Thus, the or is exclusive. Perlo calls it “aut” – either one or the other but not both:

    (M v S) & ~(M & S)

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  9. Sob, I think you are correct, I did use an empirical process (sense based) to solve the Dee/Dum puzzle and the earlier 5 hat puzzle. The following puzzle does not lend itself to using a visual aide in its solution. I read the puzzle last night and then decided to ‘sleep on it’. I woke at 3:30 this morning with the solution. Jay Ingram describes these ‘aha’ moments and believes, ‘detailed analysis of images is carried out unconsciously, even analysis that would seem to be the kind of thing that only consciousness would be capable of.’
    Here is the puzzle:
    A man lives on the twelfth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator — or if it was raining that day — he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up two flights of stairs to his apartment.

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  10. andrew said: “Here is the puzzle:
    A man lives on the twelfth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator — or if it was raining that day — he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up two flights of stairs to his apartment.”

    sounds like an interesting puzzle, andrew…what’s the question?

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  11. “A man lives on the twelfth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator — or if it was raining that day — he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up two flights of stairs to his apartment.”

    The man is too short to reach the button for the 12th floor. If it is raining he has his umbrella and can use it as an arm extender; if someone else is in the elevator he can use them as an arm extender!

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  12. andrew and perlo said: “A man lives on the twelfth floor of an apartment building…”

    thanks, you guys!!

    I would never have gotten this one…unless, of course, you started with “Alexander Pope lives on the twelfth floor of an apartment building!!”

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  13. It is so interesting, because this was presented to my colleagues & a colleague who is ‘the most’ vertically challenged person, understood it correctly…or deductively…or perceptively?

    So…does perception have much to do with one’s understanding, in this case?

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  14. a asks, “So…does perception have much to do with one’s understanding, in this case?”

    I don’t understand the question.

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  15. Well…the person who got the answer is short.

    Perhaps her perception is one of a ‘short’ person’s perception.

    I did not think of such a thing. Perhaps my perception is that of a ‘tall’ person’s perception.

    Perhaps?

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  16. Thanks, alexandra. I think you are correct in suggesting that one’s experience influences one’s understanding of the world! HNY!

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