Assignment 14

course Mth 151

I went back and studied sections 3.1 and 3.2 and understand the content much better. Understanding these sections made this section a little easier. Thanks for your help on Assignment 13.

??????????????assignment #014?w?????}??yO?????Liberal Arts Mathematics I

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

07-07-2006

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19:43:02

3.3.6 rewrite using if then ' all marines love boot camp '.

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RESPONSE -->

If it is boot camp, then marines will love it.

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19:44:28

** The statement is equivalent to 'If it's a Marine, it loves boot camp' or equivalent.

The statement is not equivalent to 'if it is boot camp, then all Marines love it', which is the converse of the original statement. **

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RESPONSE -->

Ok, I see what I did wrong. The statement is focusing on the marine and what they love.

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19:45:05

3.3.18 ~p false q false p -> q true

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RESPONSE -->

~p ^ q is true

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19:46:30

** Since ~p is false then p is true.

Since q is false it follows that p -> q is of the form T -> F, which is false.

The conditional is false when, and only when, the antecedent is true and the consequent false. **

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RESPONSE -->

Oh, I think I got this mixed up with another equation from the section. t -> f is false

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19:46:53

Query 3.3.36 write in symbols 'If play canceled, then it does not rain.'

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RESPONSE -->

p -> ~r

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19:47:26

** If p stands for 'play canceled' and r for 'it rains' then the statement would be p -> ~q. **

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RESPONSE -->

ok

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19:48:57

Query 3.3.48 q true, p and r false, evaluate and (-r U p) -> p

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RESPONSE -->

(~r v p) -> p

(T v F) -> F

T -> F

F

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19:49:14

** The antecedent (~r U p ) would be true, since ~r true and p false.

The consequent p would be false.

Since the antecedent is true and the consequent false, the conditional is false. **

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RESPONSE -->

ok

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19:51:42

Query 3.3.60 truth table for (p ^ q) -> (p U q)

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RESPONSE -->

p q (p ^ q) -> (p v q)

t t t T t

t f f T t

f t f T t

f f f T f

TTTT

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19:52:04

** The headings would be p, q ,(p^q), (pUq), (p^q)->(pUq)

Row 1 would read T T T T T

Row 2 would read T F F T T

Row 3 would read F T F T T

Row 4 would read F F F F T

The common sense of this is that whenever both p and q are true, then the statement 'p or q' must be true. That's what means to say (p ^ q) -> (p U q).

The fact that this statement is true is indicated by the last column of the truth table, which has True in every possible case. **

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RESPONSE -->

ok

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19:53:49

Query 3.3.72 negation of ' if loving is wrong then I don't want to be right'

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RESPONSE -->

Loving you is wrong and I want to be right.

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19:54:21

** The negation has to have the exact opposite truth values of the original statement.

It is difficult and confusing to try to negate a conditional. It is much easier to translate the conditional to a disjunction then negate the disjunction. It is easy to negate the disjunction using deMorgan's Laws.

Since p -> q is identical to ~p U q, the negation of p -> q is ~ ( ~p U q), which by de Morgan's Law is ~ ~p ^ ~q, or just p ^ ~q.

So the negation would ge 'loving you is wrong AND I want to be right.

COMMON ERROR AND NOTE: If loving you is wrong, then I want to be right.

INSTRUCTOR COMMENT:

The negation of a conditional can't be a conditional (a conditional is false in only one case so its negation would have to be false in three cases). **

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RESPONSE -->

ok

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19:55:08

Query 3.3.90 circuit q parallel [ p in series with ( q par. ~p) ].

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RESPONSE -->

q v [p ^ (q v ~p)]

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19:58:03

** If I'm looking at the same circuit you are the translation would be q U [ p ^ [q U ~p ]] .

Since intersection and union each distribute over the other, this would simplify to

q U [ ( p ^ q) U ( p ^ ~p) ]. Since p ^ ~p can't be true, this is the same as

q U ( p ^ q).

Since q U ( p ^ q) is true whenever q is true and false whenever q is false expression is true exactly when q is.

So the circuit finally simplifies to just q.

You should be able to see by looking at the circuit that current will flow whenever all the q switches are closed. **

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RESPONSE -->

I am just glad that I got the first part of it correct. I think I understand the next part of the problem.

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"

This looks good. Let me know if you have questions.