Assignment 31

#$&*

course mth151

012. The common sense of logic.

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

Question: `q001. Note that there are 4 questions in this assignment.

Suppose I tell you 'If it rains today, I'll give you $100.' Under which of the

following circumstances can you claim that I was not telling the truth?

1. It rains and I give you $100.

2. It rains and I don't give you $100.

3. It doesn't rain and I give you $100.

4. I doesn't rain and I don't give you $100.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

#1 only

confidence rating #$&*: very confident

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

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

Question: `q002. Suppose that tell you 'It will rain today and I will give you

$100'. Under which of the following circumstances can you claim that I was not

telling the truth?

1. It rains and I give you $100.

2. It rains and I don't give you $100.

3. It doesn't rain and I give you $100.

4. I doesn't rain and I don't give you $100.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

#2 ,#3 and #4

confidence rating #$&*: very confident

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

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

Question: `q003. Suppose that tell you 'It will rain today or I will give you

$100, but not both'. Under which of the following circumstances can you claim

that I was not telling the truth?

1. It rains and I give you $100.

2. It rains and I don't give you $100.

3. It doesn't rain and I give you $100.

4. I doesn't rain and I don't give you $100.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: #1, and #4

confidence rating #$&*: very confident

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

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

Given Solution:

In situations 2 and 3, one of the things happens and the other doesn't, so you

would not be able to say that I wasn't telling the truth. However in situation

1, both things happen, which I said wouldn't be the case; and in situation 4

neither thing happens. In both of these situations you would have to say that I

was not telling truth.

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

Question: `q004. Suppose that tell you 'It will rain today or I will give you

$100'. Under which of the following circumstances can you claim that I was not

telling the truth?

1. It rains and I give you $100.

2. It rains and I don't give you $100.

3. It doesn't rain and I give you $100.

4. I doesn't rain and I don't give you $100.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: #1 and #4

confidence rating #$&*: very confident

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

================================================================================================

012. `query 12

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

Question: `qQuery 3.1.10 Shrek is top grossing film.

Is this a statement?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

yes

confidence rating #$&*: very confident

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

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

Question: `qQuery Not assigned, but you should be able to answer: Is 'Sit up

and behave.' a statementlineCount = lineCount + 1: bLine$(lineCount) = ""

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

your solution: no one has all of the luck

confidence rating #$&*: very confident

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

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

Question: `qQuery 3.1.42 p: she has green eyes q: he is 56. What is the

statement (p disjunction q)?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: she has green eyes of he is 56

confidence rating #$&*: very confident

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

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

Question: `qQuery 3.1.48 What is the statement -(p disjunction q)

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

confidence rating #$&*:

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

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

Given Solution:

`a** The correct translation is 'It is not the case that she has green eyes or

he is 56 yrs. old'.

An equivalent statement, using deMorgan's Laws, would be 'she doesn't have green

eyes and he is 56 years old'

COMMON ERROR: She doesn't have green eyes or he is not 56 years old.

This statement negates p V q as ~p V ~q, which is not correct. The negation of

p V q is ~p ^ ~q. **

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

Self-critique (if necessary):

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

Self-critique Rating:

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

Question: `qQuery 3.1.54 Jack is an English Major or Chris collects DVDs,

and it is not the case that both are so

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

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

confidence rating #$&*: veryconfident

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

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

Question: `q3.1.68 (formerly 3.1.60). This was not assigned, but you should be

able to reason this out: {}{}True or false: there exists an integer that is

not a rational number.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: False. I looked up the proof for this.

proof : let n be any integer. (n+n)/2 is a rational number, which reduces to n.

Read more: http://wiki.answers.com/Q/Is_every_integer_an_irrational_number#ixzz1INynoGlr

confidence rating #$&*: very confident

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

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

Question: `qQuery 3.1.74 (was 3.1.66) Not assigned, but reason it out: True

or false: each rat number is a positive number.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: False. rational number is any number that can be written as a fraction of two integers. integers include negative whole numbers.

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

Question: `qQuery 3.1.75 difference between 'all students did not pass the

test' is the statement ' not all students passed the test'

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

the first statment indicates that all students did not pass. the second indicates that not all passed, but possibly some did

confidence rating #$&*: very confident

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

"

Self-critique (if necessary):

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

Self-critique rating:

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

Question: `qQuery 3.1.54 Jack is an English Major or Chris collects DVDs,

and it is not the case that both are so

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

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

confidence rating #$&*: veryconfident

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

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

Question: `q3.1.68 (formerly 3.1.60). This was not assigned, but you should be

able to reason this out: {}{}True or false: there exists an integer that is

not a rational number.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: False. I looked up the proof for this.

proof : let n be any integer. (n+n)/2 is a rational number, which reduces to n.

Read more: http://wiki.answers.com/Q/Is_every_integer_an_irrational_number#ixzz1INynoGlr

confidence rating #$&*: very confident

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

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

Question: `qQuery 3.1.74 (was 3.1.66) Not assigned, but reason it out: True

or false: each rat number is a positive number.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: False. rational number is any number that can be written as a fraction of two integers. integers include negative whole numbers.

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

Question: `qQuery 3.1.75 difference between 'all students did not pass the

test' is the statement ' not all students passed the test'

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

the first statment indicates that all students did not pass. the second indicates that not all passed, but possibly some did

confidence rating #$&*: very confident

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

"

Self-critique (if necessary):

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

Self-critique rating:

#*&!

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

Question: `qQuery 3.1.54 Jack is an English Major or Chris collects DVDs,

and it is not the case that both are so

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

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

confidence rating #$&*: veryconfident

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

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

Question: `q3.1.68 (formerly 3.1.60). This was not assigned, but you should be

able to reason this out: {}{}True or false: there exists an integer that is

not a rational number.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: False. I looked up the proof for this.

proof : let n be any integer. (n+n)/2 is a rational number, which reduces to n.

Read more: http://wiki.answers.com/Q/Is_every_integer_an_irrational_number#ixzz1INynoGlr

confidence rating #$&*: very confident

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

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

Question: `qQuery 3.1.74 (was 3.1.66) Not assigned, but reason it out: True

or false: each rat number is a positive number.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: False. rational number is any number that can be written as a fraction of two integers. integers include negative whole numbers.

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

Question: `qQuery 3.1.75 difference between 'all students did not pass the

test' is the statement ' not all students passed the test'

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

the first statment indicates that all students did not pass. the second indicates that not all passed, but possibly some did

confidence rating #$&*: very confident

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

"

Self-critique (if necessary):

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

Self-critique rating:

#*&!#*&!

&#This looks good. Let me know if you have any questions. &#