course Mth 151 ½‰ñ…„ÛÇŽE·ÑÄþⳎ{ƃX}^áëYýþassignment #013
......!!!!!!!!...................................
08:55:39 3.2.6 ~(p^q) false; truth values of components
......!!!!!!!!...................................
RESPONSE --> If it is false then p^q is true, making p and q true. confidence assessment: 3
.................................................
......!!!!!!!!...................................
08:55:45 **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.**
......!!!!!!!!...................................
RESPONSE --> OK self critique assessment: 3
.................................................
......!!!!!!!!...................................
08:57:52 3.2.18 p false q true ~[(~p^~q) U ~q]
......!!!!!!!!...................................
RESPONSE --> (~p ^ ~q) is false because ~q is false. since ~q is false, that makes both parts[(~p^~q) U ~q] false. [(~p^~q) U ~q] is also false. confidence assessment: 3
.................................................
......!!!!!!!!...................................
08:58:01 **~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.**
......!!!!!!!!...................................
RESPONSE --> OK self critique assessment:
.................................................
......!!!!!!!!...................................
09:00:14 3.2.36 p: 2>7 q: 8 not > 6 r: 19 <= 19 evaluate -(p U -q) U -r
......!!!!!!!!...................................
RESPONSE --> p and q are false, r is true. So p U ~q is true: since ~q is true ~(p U ~q) is false. r is true, so ~r is false. The disjunction of the two statements are false, so the whole thing is false. confidence assessment: 3
.................................................
......!!!!!!!!...................................
09:00:28 ** 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. **
......!!!!!!!!...................................
RESPONSE --> OK self critique assessment:
.................................................
......!!!!!!!!...................................
09:03:37 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.
......!!!!!!!!...................................
RESPONSE --> Two statements give TT, TF, FT and FF. Three statements give TTT, TTF, TFT, TFF, and FTT, FTF, FFT, FFF. The number of truth values for 2 statements is 4, For 3 statements, the value is 8 You use 2^n to find the total values, so with the 8 that gives: 256 possible truth values. confidence assessment: 3
.................................................
......!!!!!!!!...................................
09:04:10 ** 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. **
......!!!!!!!!...................................
RESPONSE --> ok self critique assessment:
.................................................
......!!!!!!!!...................................
09:04:41 3.2.54 truth table for (-p ^ -q) U (~p U q)
......!!!!!!!!...................................
RESPONSE --> first:T T F F F T T. second: T F F T F F F third: F T T F F T T fourth: F F T T T T T confidence assessment:
.................................................
......!!!!!!!!...................................
09:04:54 ** 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 **
......!!!!!!!!...................................
RESPONSE --> OK self critique assessment: 3
.................................................
......!!!!!!!!...................................
09:07:28 3.2.66 negate using De Morgan's Law: ' V.M. tried to sell the book but she was unable to do so'.
......!!!!!!!!...................................
RESPONSE --> V.M. didn't try to sell the book or she sold it confidence assessment: 3
.................................................
......!!!!!!!!...................................
09:07:49 ** 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. **
......!!!!!!!!...................................
RESPONSE --> OK self critique assessment: 3
.................................................
......!!!!!!!!...................................
09:08:04 3.2.78 is the statement 3 + 1 = 4 xor 2 + 5 = 9 true or false?
......!!!!!!!!...................................
RESPONSE --> The statement is true because the first part is true and the second is false. confidence assessment: 3
.................................................
......!!!!!!!!...................................
09:08:15 ** 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. **
......!!!!!!!!...................................
RESPONSE --> OK self critique assessment: 3
................................................."