course Mth 151 O CèȴyvԚXIb assignment #013
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16:22:24 3.2.6 ~(p^q) false; truth values of components
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RESPONSE --> If the opposite of p and q is false, then both must be true confidence assessment: 2
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16:22:36 **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 self critique assessment: 3
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16:23:52 3.2.18 p false q true ~[(~p^~q) U ~q]
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RESPONSE --> ~p^~q is false, and ~q is false, so the opposite must be true confidence assessment: 3
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16:23:57 **~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 self critique assessment: 3
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16:27:31 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 is false, ~q is true, and ~r is false, so if ~q is one of the possibilities, then this is true. confidence assessment: 2
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16:28:35 ** 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 --> I thought that ~(p U ~q) would be true, but I understand the mistake I made self critique assessment: 2
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16:32:15 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 --> There are 8 components, so the number of rows will be 2^n, which is 2^8 = 256 confidence assessment: 2
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16:32:23 ** 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 --> OK self critique assessment: 3
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16:32:47 3.2.54 truth table for (-p ^ -q) U (~p U q)
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RESPONSE --> T,F,T,T confidence assessment: 3
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16:33:52 ** 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 --> That's the result that I got; I wrote down the final column from top to bottom instead of writing the row from left to right. self critique assessment: 2
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16:34:24 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 --> V.M did not try to sell the book, or she was unable to do so confidence assessment: 2
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16:34:57 ** 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 --> OK self critique assessment: 2
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16:35:20 3.2.78 is the statement 3 + 1 = 4 xor 2 + 5 = 9 true or false?
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RESPONSE --> True, because 3+1=4 is true and 2+5=9 is false confidence assessment: 3
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16:35:28 ** 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 --> OK self critique assessment: 3
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