Query Ass 13

course Mth 151

ÈãÅÖÎÊLê½ØõÛ€léIœº¹èŽassignment #013

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013. `query 13

College Algebra

02-25-2007

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20:15:41

3.2.6 ~(p^q) false; truth values of components

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RESPONSE -->

false

I just want to let you know that I am sort of lost right now on these question. I fully understand the truth tables but I am not sure how to get the correct answers for these next few.

confidence assessment: 1

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20:17:22

**The question asks for the truth values of p and q that would make the statement ~(p^q) false. If ~(p^q) is false then p^q is true, which means that both p and q must be true.**

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RESPONSE -->

I gather that concept. I was trying to read it all together and not break it down

self critique assessment: 3

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20:17:55

3.2.18 p false q true ~[(~p^~q) U ~q]

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RESPONSE -->

I put false

confidence assessment: 1

You need to explain your reasoning. Especially on these questions where you have a 50-50 chance of answering correctly by just guessing. I don't think you're just guessing; the point is I need to see what you're thinking, and I can't tell by just a 'true' or 'false' answer.

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20:21:13

**~p ^ ~q is false because ~q is false. One false is fatal to a conjunction.

~q is false so both parts of the disjunction [(~p^~q) U ~q] are false. Thus [(~p^~q) U ~q] is false.

The negation ~[(~p^~q) U ~q] of this statement is therefore true.**

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RESPONSE -->

I guess I am just reading too much into these questions. However, I understand that one false and one true cannot make a conjunction but couls a disjunction

self critique assessment: 3

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20:23:49

3.2.36 p: 2>7 q: 8 not > 6 r: 19 <= 19 evaluate -(p U -q) U -r

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RESPONSE -->

It would be true

confidence assessment: 1

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20:25:52

** p and q are both false statements, while r is a true statement.

It follows that p U ~q is true: since ~q is true the disjunction is true.

It therefore follows that ~(p U ~q) is false.

Since r is true, ~r is false.

Thus ~(p U ~q) U ~r is a disjunction of two false statements, ~(p U ~q) and ~r.

A disjunction of two false statements is false.

So the statement is false. **

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RESPONSE -->

Ah, okay. I put false in my text answers but was unsure.

self critique assessment: 3

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20:28:10

3.2.42 How many rows are there in a statement involving p,q,r,s,u,v,m,n? Note that rows go across the page. For example a statement involving just p and q will have four rows, one each for TT, TF, FT and FF. The headings (i.e., p, q and whatever other statements are necessary to evaluate the truth table) might also be considered a row, but for this problem do not consider the headings to be a row.

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RESPONSE -->

32?

confidence assessment: 3

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20:28:55

** If you just have two statements p and q, then there are four possible truth values: TT, TF, FT and FF.

If you have three statements p, q and r then there are eight possible truth values: TTT, TTF, TFT, TFF, and FTT, FTF, FFT, FFF.

Note that the number of possible truth values doubles every time you add a statement.

The number of truth values for 2 statements is 4, which is 2^2.

For 3 statements this doubles to 8, which is 2^3.

Every added statement doubles the number, which adds a power to 2.

From this we see that the number of possible truth values for n statements is 2^n.

For the 8 statements listed for this problem, there are therefore 2^8 =256 possible truth values. **

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RESPONSE -->

I just added four to every statement

self critique assessment: 3

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20:32:06

3.2.54 truth table for (-p ^ -q) U (~p U q)

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RESPONSE -->

p, q, -p, -q, (-p^-q), (-p v q), (-p^-q) v (-p v q)

confidence assessment: 3

Good job on the headings.

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20:32:38

** For column headings

p q ~p ~q ~p^~q ~p U q (~p^~q) U (~p Uq)

the first row would start off T T, for p and for q. Then F F for ~p and ~q. Then F for ~p ^ ~q, then T for ~p V q, then T for the final column.

So the first row would be

T T F F F T T.

The second row would be

T F F T F F F

The third row would be

F T T F F T T

and the fourth row would be

F F T T T T T **

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RESPONSE -->

gotcha

self critique assessment: 3

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20:33:35

3.2.66 negate using De Morgan's Law: ' V.M. tried to sell the book but she was unable to do so'.

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RESPONSE -->

P.V. did not try to sell the book and was able to do so

confidence assessment: 3

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20:34:01

** We use two ideas here. The first is that 'but' is interpreted as 'and'; and the second is that the negation of an 'and' statement is an 'or' statement. deMorgan's Laws say that the negation of p OR q is ~p AND ~q, while the negation of p AND q is ~p OR ~q.

The given statement ' V.M. tried to sell the book but she was unable to do so' can be symbolized as 'p ^ q'. Its negation would be ~(p ^ q) = ~p U ~q. We translate this as 'V.M. didn't try to sell the book or she sold it', or something equivalent. **

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RESPONSE -->

self critique assessment:

Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the given solution, and if necessary asking specific questions.

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20:34:58

3.2.78 is the statement 3 + 1 = 4 xor 2 + 5 = 9 true or false?

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RESPONSE -->

true because bothe statements are not true, but one is

confidence assessment: 3

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20:35:09

** For an XOR statement exactly one part has to be true. The statement is true because the first part is true and the second is false.

We need exactly one true statement; if both parts were true the XOR wouldn't be. **

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RESPONSE -->

okay

self critique assessment: 3

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"

I think you've got the general idea, but I need to see more detail in your answers.