Assign 14

course Mth 151

r???D???z??m??assignment #014

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014. Truth Tables

Liberal Arts Mathematics I

10-13-2007

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14:02:10

`q001. There are 8 questions in this set.

If each of the propositions p and q can be either true or false, what combinations of truth values are possible for the two propositions (e.g., one possibility is that p is false and q is true; list the other possibilities)?

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RESPONSE -->

p true q true

p ture q false

p false q false

confidence assessment: 2

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14:02:44

It is possible that p is true and q is true.

Another possibility is that p is true and q is false.

A third possibility is that p is false and q is true.

A fourth possibility is that p is false and q is false.

These possibilities can be listed as TT, TF, FT and FF, where it is understood that the first truth value is for p and the second for q.

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RESPONSE -->

I used the truth tables you show on the DVD.

self critique assessment: 2

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14:05:10

p ^ q means 'p and q', which is only true if both p and q are true.

In the case TT, p is true and q is true so p ^ q is true.

In the case TF, p is true and q is false so p ^ q is false.

In the case FT, p is false and q is true so p ^ q is false.

In the case FF, p is false and q is false so p ^ q is false.

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RESPONSE -->

I hit some in doing my answer so I just put it in here. Then looked at your explanation.

p true q false

p true q true

p false q true

p false q false

self critique assessment: 3

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14:07:43

`q003. Write the results of the preceding problem in the form of a truth table.

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RESPONSE -->

p true q true p ^ q true

p ture q false p ^ q false

p false q true p ^ q false

p false q false p ^ q false

confidence assessment: 2

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14:08:07

The truth table must have headings for p, q and p ^ q. It must include a line for each of the possible combinations of truth values for p and q. The table is as follows:

p q p ^ q

T T T

T F F

F T F

F F F.

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RESPONSE -->

I wasn't sure that that was what you were asking but I see that it was.

self critique assessment: 2

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14:31:11

`q004. For each of the possible combinations TT, TF, FT, FF, what is the truth value of the proposition p ^ ~q?

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RESPONSE -->

F, F, T, F. I went by the combined statement table

confidence assessment: 1

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14:32:10

For TT we have p true, q true so ~q is false and p ^ ~q is false.

For TF we have p true, q false so ~q is true and p ^ ~q is true.

For FT we have p false, q true so ~q is false and p ^ ~q is false.

For FF we have p false, q false so ~q is true and p ^ ~q is false.

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RESPONSE -->

self critique assessment: 1

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14:48:37

`q005. Give the results of the preceding question in the form of a truth table.

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RESPONSE -->

T, F, F, F

confidence assessment: 2

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14:49:25

The truth table will have to have headings for p, q, ~q and p ^ ~q. We therefore have the following:

p q ~q p^~q

T T F F

T F T T

F T F F

F F T F

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RESPONSE -->

I used the wrong table.

self critique assessment: 1

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15:09:22

`q006. Give the truth table for the proposition p U q, where U stands for disjunction.

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RESPONSE -->

TT, T

TF, T

FT, T

FF, F

confidence assessment: 2

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15:10:05

p U q means 'p or q' and is true whenever at least one of the statements p, q is true. Therefore p U q is true in the cases TT, TF, FT, all of which have at least one 'true', and false in the case FF. The truth table therefore reads

p q p U q

T T T

T F T

F T T

F F F

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RESPONSE -->

Since one of them in all the groups except the last group they are all true.

self critique assessment: 2

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15:11:45

`q007. Reason out the truth values of the proposition ~(pU~q).

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RESPONSE -->

would all be false because p and q would be in the groups

confidence assessment: 1

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15:12:58

In the case TT p is true and q is true, so ~q is false. Thus p U ~q is true, since p is true. So ~(p U ~q) is false.

In the case TF p is true and q is false, so ~q is true. Thus p U ~q is true, since p is true (as is q). So ~(p U ~q) is false.

In the case FT p is false and q is true, so ~q is false. Thus p U ~q is false, since neither p nor ~q is true. So ~(p U ~q) is true.

In the case FF p is false and q is false, so ~q is true. Thus p U ~q is true, since ~q is true. So ~(p U ~q) is false.

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RESPONSE -->

I forgot about the one that didn't contant either.

self critique assessment: 2

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15:17:29

`q008. Construct a truth table for the proposition of the preceding question.

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RESPONSE -->

T

T

F

T

confidence assessment: 1

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15:17:54

We need headings for p, q, ~q, p U ~q and ~(p U ~q). Our truth table therefore read as follows:

p q ~q pU~q ~(pU~q)

T T F T F

T F T T F

F T F F T

F F T T F

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RESPONSE -->

I wasn't sure if I did it right or not.

self critique assessment: 1

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Self-critique should be included here.

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Try to be more detailed in showing the details of your reasoning, and when self-critique is necessary be sure to address the details there as well.

In any case you're doing OK; if you provide more detail I can help clarify things for you.