course Mth 151 I am going to have to review the DVD and the section again. This section gave me a fit, as I am sure you can tell ???????|???assignment #013013. `query 13
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07:46:51 3.2.6 ~(p^q) false; truth values of components
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RESPONSE --> TT, TF, FT confidence assessment: 3
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07:47:50 **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 gave a false value too instead of just the true values. self critique assessment: 2
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07:56:09 3.2.18 p false q true ~[(~p^~q) U ~q]
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RESPONSE --> False confidence assessment: 1
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x?m?????W?w?? assignment #013 013. `query 13 College Algebra 10-14-2007
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09:09:44 3.2.6 ~(p^q) false; truth values of components
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RESPONSE --> TT because you would have to have p and q. confidence assessment: 2
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09:10:58 **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 --> You work the ( ) first and in order for those to be they each are true. self critique assessment: 2
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09:18:55 3.2.18 p false q true ~[(~p^~q) U ~q]
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RESPONSE --> false becuase you have p true confidence assessment: 1
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09:23:22 **~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 --> Working through the tables help but are confusing at the same time. self critique assessment: 1
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09:47:55 3.2.36 p: 15<8 q: 9 not > 5 r: 18 <= 18 evaluate -(p U -q) U -r
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RESPONSE --> True. confidence assessment: 1
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09:49:56 ** 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 --> The explanations are helping know what I have done wrong. I started off wrong, I put that ~q was false. self critique assessment: 3
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09:59:02 (formerly 3.2.42) This wasn't assigned, but you should be able to answer based on your responses to similar assigned questions. {}{}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 because you have 4 for each letter. confidence assessment: 2
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10:00:16 ** 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 mutiplied 8 *4. I didn't do 2^8. self critique assessment: 1
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10:15:42 3.2.56 (fomerly 3.2.54) This was not assigned but based on your work on similar problems you should be able to construct the truth table for (-p ^ -q) U (~p U q). Give your truth table:
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RESPONSE --> TTFFTFF TFFFTFF FTTFTTT FFTTFFT confidence assessment: 3
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10:18:45 ** 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 --> My colunm headings were p q ~p ~p^~q pUq ~pUq (~p^~q)U(~pUq). self critique assessment: 2
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10:22:35 3.2.68 (formerly 3.2.66) This wasn't assigned but is similar to other assigned problems so you should be able to solve it: Negate the following statement using De Morgan's Law: ' F.C. tried to sell the wine but was unable to do so'.
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RESPONSE --> FC did not try to sell the wine so he was not able to sell the wine. confidence assessment: 2
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10:23:08 ** 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 ' F.C. tried to sell the book but was unable to do so' can be symbolized as 'p ^ q'. Its negation would be ~(p ^ q) = ~p U ~q. We translate this as 'F.C. didn't try to sell the book or he sold it', or something equivalent. **
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RESPONSE --> self critique assessment: 2
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10:23:54 3.2.81 is the statement 3 + 1 = 6 xor 2 + 5 = 7 true or false?
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RESPONSE --> true becuase the word or and 2+5=7 is true. confidence assessment: 2
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10:24:31 ** For an XOR statement exactly one part has to be true. The statement is true because the second part is true and the first is false. We need exactly one true statement; if both parts were true the XOR wouldn't be. **
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RESPONSE --> Since one part was true the statement was true. self critique assessment: 2
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