course Mth 151 Watch out Mr. Smith, you'll get a good laugh or a headache checking this assignment. I have to say that this is my absolute least favorite assignment to date (and that is honestly saying a lot because math is not my thing). þ»¤Lá]ÞùÆÝÔŸÒÕ¦Žƒassignment #013
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20:37:01 3.2.6 ~(p^q) false; truth values of components
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RESPONSE --> ~(p^q) p^q must be true for the opposite or negation to be false. p=T q=T
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20:37:11 **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 --> ok
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20:39:21 3.2.18 p false q true ~[(~p^~q) U ~q]
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RESPONSE --> ~[(F ^ ~T) v ~T)] ~[F v ~T] ~[F] T
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20:39:48 **~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 --> ok
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20:42:45 3.2.36 p: 2>7 q: 8 not > 6 r: 19 <= 19 evaluate -(p U -q) U -r
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RESPONSE --> p = F (because 2 > 7 is not true) q = F (because 8 is greater than 6) r = T (because 19 is equal to 19) ~(p v ~q) v ~r ~(F v ~F) v ~T ~(T) v ~T F v F F
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20:43:04 ** 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 --> ok
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20:46:49 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 --> Since there are eight letters, use the equation 2n (little n at the top) to figure the rows. 2(8) - 8 being at the top right of 2 = 256 rows
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20:47:44 ** 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 forgot about the little carot symbol. 2^8 = 256
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20:56:35 3.2.54 truth table for (-p ^ -q) U (~p U q)
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RESPONSE --> Ok, here is what I got. I didn't finish. p q ~p ~q ~p ^ ~q ~p v q T T F F F T F F T T F T T F T F F T T T Now, how I got this far I'm not even sure. I can't explain it. It probably isn't right.
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21:00:32 ** 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 --> I have watched the videos and read the book, but it still doesn't make much sense to me. I got some of it correct (the easy stuff like ~p and ~q), but the other is still hard. Maybe I'll try watching the videos again.
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21:01:41 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 --> Pauline Mula did not try to sell the book and she was unable to do so. (This confuses me a little, too)
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21:06:29 ** 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 --> Your explanation is easier to understand than what is in the book, but I think it will take a minute to sink in. p ^ q = ~(p v q)
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21:08:59 3.2.78 is the statement 3 + 1 = 4 xor 2 + 5 = 9 true or false?
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RESPONSE --> I didn't understand exclusive disjunction. I didn't get number 75 where we had to fill out the truth table for the exclusive disjunction and this problem builds on that one so I definately didn't get number 78.
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21:09:31 ** 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 --> I don't really understand that.
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