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course Mth 151

ܩ־FϤPEpNassignment #014

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014. Truth Tables

Liberal Arts Mathematics I

06-26-2007

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20:11:34

`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 is true and q is true; p is true and q is false; p is false and q is true; p is false and q is false

confidence assessment: 3

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20:11:42

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 -->

OK

self critique assessment: 3

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20:12:25

`q002. For each of the for possibilities TT, TF, FT and FF, what is the truth value of the compound statement p ^ q ?

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RESPONSE -->

For TT the truth value is T;

For TF the truth value is F:

For FT the truth value is F;

For FF the truth value is F

confidence assessment: 3

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20:12:33

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 -->

OK

self critique assessment: 3

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20:13:44

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

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RESPONSE -->

The possibilites for p are T,T,F,F

The possibilities for Q are T,F,T,F

p^q is T,F,F,F

confidence assessment: 3

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20:14:12

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 what the appropriate way to represent a truth table would be using the computer

self critique assessment: 2

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20:14:47

`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,T,F,F

confidence assessment: 3

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20:14:54

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 -->

OK

self critique assessment: 3

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20:16:00

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

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RESPONSE -->

p q ~q p^~q

T T T F

T F F T

F T F F

F F F F

confidence assessment: 3

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20:16:15

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 -->

OK

self critique assessment: 3

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20:17:32

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

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RESPONSE -->

p q pUq

T T T

T F T

F T T

F F F

confidence assessment: 3

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20:17:38

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 -->

OK

self critique assessment: 3

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20:18:46

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

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RESPONSE -->

pU~q would be T,T,F,T so ~(pU~q) is F,F,T,F

confidence assessment: 3

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20:18:56

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 -->

OK

self critique assessment: 3

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20:20:46

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

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RESPONSE -->

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

confidence assessment: 3

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20:20:52

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 -->

OK

self critique assessment: 3

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