assignment 14

course mth 151

i think this coming week will be better. my grandmother's health got worse so I had to go back out of town. Hope this makes it in time. Thanks.

?z????????????€Student Name:

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assignment #014

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15:37:25

`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 -->

true, false

true, true,

false, false

false, true

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15:37:28

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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15:38:23

`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 p is true and q is true

for tf p is true and q is false

for ft p is false and q is true

for ff p is false and q is false

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15:38:26

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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15:38:53

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

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RESPONSE -->

p^q

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15:39:04

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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15:40:58

`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 -->

p is true but ~q is false

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15:41:22

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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i'm sorry i forgot the rest

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15:42:31

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

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RESPONSE -->

p q

t t

t f

f t

f f

p^~q

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15:43:04

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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these tables confuse me but i see what i did wrong

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15:44:27

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

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p q

t t

t f

f t

f f

p U q

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15:44:43

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

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15:45:20

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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i must have hit enter too soon i didn't see ?7

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15:45:43

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

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i'm not sure what the preceding question was

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15:45:56

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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assignment 14

More detail would be a good idea, along with self-critique, but it appears that you understand most of the important ideas.