quote:

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A landscape designer wishes to use roses of different colours in a large planter. Seven colours of roses are available for selection: lavender, orange, pink, red, tan, white, and yellow. Only certain colour combinations will be used based on the following conditions:

If lavender is used, then so is tan.
If red is used, then yellow is not used.
If orange, tan, or both are used, then so is red.
If pink is not used, then neither is lavender.
If white is not used, then yellow is used.

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So I've set it up as the following in my notebook

code:

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 Used           Not
L --> T
R--------------> Y
O/T --> R
               P --> L
Y <------------- W

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The question is, "If Tan is not used, which one of the following must be true?"
(A) Pink is not used
(B) Either lavender or red is used
(C) Orange and red are the only two colours used.
(D) Either white or yellow or both are used
(E) Both red and yellow are used

The answer is (D). If T is not used, then L is not used. Since L is not used, P may or may not be used; therefore, answer (A) is incorrect. Since R may or may not be used, answer (B) is incorrect. Since R does not have to be used, answers (C) and (E) are incorrect. It is not possible for both W and Y not to be used; therefore, answer (D) is correct.

I couldn't figure it out on my own because I can't grasp the logic behind the contrapositives. Example, if lavender is used then so is tan, would turn into, if tan is not used then lavender is not used. I get why L can't be used because T is not used. What I don't understand how P has the possibility of being used. 'If pink is not used, then lavender is not used'. So wouldn't it also be true 'if lavender is used, then pink is used'? And since lavender can't be used, pink can't be used, correct?

quote:

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Mr. Parcelan wrote, obviously thinking too hard:
kill all nerds

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Without us, on the off chance you survived childbirth, you would die a slow unforgiving death in a harsh desolate world with no hope of a future.

p q p->q

T T T
T F F
F T T
F F T

It's a true implication if both statements are true and if the first statement is false. It's only a false implication if the first statement is true, but the second statement is false.

For the last two, we don't know what happens when the first statement is false. We only can reliably predict the validity of the implication based on the first statement being true.

So to apply this, we're assuming that these are valid implications. This means we can't have an instance where the first statement is true, but the second is false.

So for the first statement, if it's true that lavender is used, then it's true that tan is used. We're assuming a valid implication, so it's never true that when lavender is used, tan isn't used. But we know nothing about what happens when lavender isn't used.

However, in the question, we know for sure that the statement that tan is used is false. Still assuming this is a true implication, this is only possible when it's false that lavender is used.

If you apply these same rules to the other statements, you can see that the only one we can definitively say for sure is true is (D), still assuming that we want the implication to be true.

If it's true that white isn't used, then it's true that yellow is used. If white not being used is false, meaning that white IS used, then it could be true or false that yellow is used, and either will result in a true implication.

So either white isn't used and yellow is used alone, or white is used, and white is either used alone or white is used with yellow. The last statement's wording requires that at least one of those colors be present.

Symbolic logic can be a real bear to wrap your mind around. What are you taking an entry test over?

We know from the first statement it's true that lavender isn't used. This will make a true implication when it's either true that pink isn't used or when it's false that pink isn't used.

Lyinar Ka`Bael fucked around with this message on 11-07-2011 at 09:39 PM.