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mth 151
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
chapter 3 truth tables
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OK! Issue with test was understanding of truth tables. Is there a good example I have going through your homework, the book, and you tube video's still have issues. I like step one do this or like elementary school basic steps.
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There are just a few rules for evaluating your basic instructions.
The truth value of the negation ~p is the opposite of the truth value of p.
The truth value of the conjunction p ^ q is true if both p and q are true, otherwise it's false.
The truth value of the disjunction p V q is false of both p and q are false, otherwise it's true.
The truth value of the conditional p -> q is false if p is true but q is false, otherwise it's true.
You have to understand these rules to begin using truth tables. I'll note that on your test you were on the right track, but you didn't apply these rules correctly.
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pV(-q/\r) give number of rows in truth statement. Then after rows how is third and fourth row getting t/f for 1st row is 1to 4 true then 5 to 8 false and second row true then false that repeats. third and forth lost.
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It's clear that you're making a real effort. In reviewing your portfolio page, though, I find that you haven't been submitting the QA's and Queries for this chapter. These are important exercises, especially valuable for getting my feedback and assistance. I do recommend that you work through and submit them.
Regarding the expression
p V (~q ^ r )
each of the expressions p, q and r can be true or false. So it's possible to have all three true, or all three false, or any mix of true and false.
If you list all the possible true-false combinations for p, q and r, you will find that there are eight, namely
TTT
TTF
TFT
TFF
FTT
FTF
FFT
FFF
So we have eight rows, each with a different set of truth values. We can put a heading line at the top of our list to help us keep track of our statements, so at this point our table reads
pqr
TTT
TTF
TFT
TFF
FTT
FTF
FFT
FFF
The statement p V (~q ^ r ) includes ~q, so we need to find the value of ~q for each row.
The value of q is second value listed (for the row TTT the value of q is T, for the row TTF the value of q is T, for the row TFT the value of q is F, etc.) . So we expand each row to include the value of ~q, giving us the table
pqr~q
TTTF
TTFF
TFTT
TFFT
FTTF
FTFF
FFTT
FFFT
Now to evaluate p V (~q ^ r) we need to first figure out the value of conjunction ~q ^ r. This is easily done. The rule for ^ is that it's true if the two statements of the conjunction are both true, and false otherwise. So to evaluate ~q ^ r for each line, we need only look at the values of r and ~q.
We see that in the first line r is true, but ~q is false. So ~q ^ r is false, and our first line will now read TTTFF. The same is true for the second line, which will now read TTFFF. In the third line, though, both r and ~q are true, so ~q ^ r is true. So the third line will now read TFTTT.
We continue in the same way until we get to the last line. Our truth table will now read
pqr~q ~q ^ r
TTTF F
TTFF F
TFTT T
TFFT F
FTTF F
FTFF F
FFTT T
FFFT F
Finally, we have lines for both p and (~q ^ r) so we can evaluate p V (~q ^ r). For each row we need only look at the values of p and (~q ^ r). The rule for disjunction V is that the disjunction is false if both statements are false, otherwise it's true.
In the first row p is true and ~q ^ r is false. Since these statements are not both false, the disjunction is true and our row will read TTTF F T. We analyze each line by looking at the values of p and ~q ^ r, and we obtain the final table
pqr~q ~q ^ r p V (~q ^ r)
TTTF F T
TTFF F T
TFTT T T
TFFT F T
FTTF F F
FTFF F F
FFTT T T
FFFT F F
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Check my notes above. Note also my recommendation that you submit the qa's and queries so I can give you consistent assistance and feedback.
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