assignment 14 qa

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course MTH 151

10/20 around 11:45

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

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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 q

t t

t f

f t

f f

confidence rating #$&*: 3

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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.

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Self-critique (if necessary):ok

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Self-critique Rating:ok

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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:

p^q is a conjunction and must not contain any false statements to be true

tt=true

tf=false

ft=false

ff=false

confidence rating #$&*: 3

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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.

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Self-critique (if necessary):ok

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Self-critique Rating:ok

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

p q p^q

t t t

t f f

f t f

f f f

confidence rating #$&*: 3

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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.

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Self-critique (if necessary):ok

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Self-critique Rating:ok

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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:

p for each statement is as stated

tt= q would be negated and therefore be false and would make the conjunction false

tf= ~q would be true, the conjunction would be true

ft= p is false and ~q is false so the sonjunction is false

ff= p is false even though ~q is true the conjunciton is still false

confidence rating #$&*: 3

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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.

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Self-critique (if necessary):ok

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Self-critique Rating:ok

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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

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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

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Self-critique (if necessary):ok

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Self-critique Rating:

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

p q pVq

t t t

t f t

f t t

f f f

at least one statement must be true in order for the disjunction to be true

confidence rating #$&*: 3

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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

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Self-critique (if necessary):ok

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Self-critique Rating:ok

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

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Your solution:

p q ~q pV~q ~(pV~q)

t t f t f

t f t t f

f t f f t

f f t t f

1.tt

so ~q=false. pV~q is true since p is true so its negagtion is false

2.tf

~q=true. pV~q is true since both are true. its negation is false

3.ft

~q=false. pV~q=false since both are false so its negation is true

4.ff

~q=true. pV~q=true since ~q is true so its negation is false

confidence rating #$&*: 3

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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.

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Self-critique (if necessary):ok

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Self-critique Rating:ok

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

p q ~q pV~q ~(pV~q)

t t f t f

t f t t f

f t f f t

f f t t f

confidence rating #$&*: 3

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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

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Self-critique (if necessary):ok

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Self-critique Rating:ok

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

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 #$&*:

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

p q ~q (p^~q) q V (p^~q)

t t f f t

t f t t t

f t f f t

f f t f f

confidence rating #$&*:

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

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Self-critique Rating:ok

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&#Very good work. Let me know if you have questions. &#