second assignment

(Back to course page.)

Answer the following questions. Type up your answers, print them out, and turn them in on Monday the 28th. This is a good chance for you to see how well your grokking the material so far. I suggest doing them on your own so you can accurately gauge what you need to work on. Feel free to see me if you need help.

  1. Of the following conditions, one is necessary for being a rectangle and the other is sufficient. Which is which?

    1. Being a four-sided closed figure.
    2. Being a square.

  2. Provide two counterexamples to the following analysis of water, one showing that the conditions together are not sufficient and one showing that they are not necessary.

    • Something is water if and only if (1) it is clear, (2) it is potable, and (3) it is a liquid.

  3. Is the following argument valid? Is it sound? (If it’s not valid, provide a counterexample. If it’s not sound, say why)

    1. In order to distinguish rotten apples from fresh ones, one needs criteria of rotten apples.

    2. In order to find criteria of rotten apples, one needs to be able to distinguish rotten apples from fresh ones.

      Therefore,

    3. One cannot distinguish rotten apples from fresh ones.

  4. The following is a list of three premises. The goal is to find the appropriate conclusion:

    1. All babies are illogical.
    2. Nobody is despised who can manage a crocodile.
    3. Illogical persons are despised.

    In this case, the conclusion to be drawn is “No baby can manage a crocodile.” (See how that’s a valid argument? See how I got the conclusion?) Not so hard, right? Now try your hand at this one:

    1. None of the unnoticed things, met with at sea, are mermaids.
    2. Things entered in the log, as met with at sea, are sure to be worth remembering.
    3. I have never met with anything worth remembering, when on a voyage.
    4. Things met with at sea, that are noticed, are sure to be recorded in the log.

    What’s conclusion is to be drawn? Now try this one:

    1. No interesting poems are unpopular among people of real taste.
    2. No modern poetry is free from affectation.
    3. All your poems are on the subject of soap-bubbles.
    4. No affected poetry is popular among people of real taste.
    5. No ancient poem is on the subject of soap-bubbles.

    What’s the conclusion to be drawn?

    (These are classic logic puzzles from Lewis Carroll. I’m sure you could look up the answers on the internet; but what would be the point? It’s OK with me if you can’t find the answers, so why deprive yourself of the fun of trying?)

  5. Finally, construct an argument showing that there can be no barber who shaves all and only those who don’t shave themselves. (Hint: let the first premise be “If there is such a barber, he either shaves himself or does not shave himself.” It took me six premises to get to the conclusion.)