Assignment 14

#$&*

course MTH 151

04/05/2014 at 2:28Professor,

I know I am a bit behind, but I am in the process of catching up on everything. I've had some personal problems, but I have worked through them and am getting back on track. I know you probably don't want to receive all of my homework submissions at once, so I will be submitting each as I finish. I am more of a numbers math person, so these chapters are a little more difficult for me, but I am understanding it to the best of my ability.

I just wanted to assure you that I am continuing to work on my assignments and want to succeed in this course.

Thank you for your time and understanding,

Heidi" "If your solution to stated problem does not match the given solution, you should self-critique per instructions at

 

   http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

.

Your solution, attempt at solution.  If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it.  This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

 

 

014. Truth Tables

 

 

*********************************************

Question: `q001. There are 10 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)?

 

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

p is false, q is false.

p is true, q is true.

p is false, q is true.

p is true, q is false.

(FF, TT, FT, TF)

 

 

confidence rating #$&*: 3.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

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.

 

 

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 

 

------------------------------------------------

Self-critique Rating:

*********************************************

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

 

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Referring to the truth table for ^ (and); TT=T, TF=F, FT=F, FF=F. So, only if p is true and q is true, will the statement be true.

 

 

confidence rating #$&*: 3.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

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.

 

 

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 

 

------------------------------------------------

Self-critique Rating:

*********************************************

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

 

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

As I used in the previous problem:

p q | p^q

T T | T

T F | F

F T | F

F F | F

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

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.

 

 

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 

 

------------------------------------------------

Self-critique Rating: 3.

*********************************************

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

 

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The problem will read “p and the negation of q”.

So, TT (p is true and q is true, so ~q is false), so TT will become TF, which is false.

TF (p is true and q is false, so ~q is true), so TF will become TT, which is true.

FT (p is false and q is true, so ~q is false), so FT will become FF, which is false.

FF (p is false and q is false, so ~q is true), so FF will become FT, which is false.

 

 

confidence rating #$&*: 3.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

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.

 

 

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 

 

------------------------------------------------

Self-critique Rating:

*********************************************

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

 

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

p q ~q | p^~q

T T F | F

T F T | T

F T F | F

F F T | F

 

 

confidence rating #$&*: 3.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

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

 

 

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 

 

------------------------------------------------

Self-critique Rating:

*********************************************

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

 

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

p q | pUq

T T | T

T F | T

F T | T

F F | F

 

 

confidence rating #$&*: 3.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

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

 

 

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 

 

------------------------------------------------

Self-critique Rating:

*********************************************

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

 

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

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

So, p is false and q is true makes ~(pU~q) true.

 

 

confidence rating #$&*: 3.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

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.

 

 

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 

 

------------------------------------------------

Self-critique Rating:

*********************************************

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

 

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

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 rating #$&*: 3.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

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

 

 

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 

 

------------------------------------------------

Self-critique Rating:

 

*********************************************

Question: `q009.  Construct a truth table for the statement (p ^ ~q).

(p^~q) is p and ~q

p q ~q | (p^~q)

T T F | F

T F T | T

F T F | F

F F T | F

If p is true and q is false (which means ~q is true), then (p^~q) is true.

 

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: 3.

 

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

*********************************************

Question: `q010.  Construct a truth table for the statement q U (p ^ ~q).

 

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

I used my table from the previous problem first:

p q ~q | (p^~q) p U (p^~q)

T T F | F T

T F T | T T

F T F | F F

F F T | F F

Or means at least one part of the problem has to be true. TF=T, TT=T, FF=F, FF=F.

@&

This question asked about q U ( p ^ ~q ).

In any case it seems that you understand this.

*@

 

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

------------------------------------------------

Self-critique Rating:

&#Your work looks good. See my notes. Let me know if you have any questions. &#