Text Assignment 3-3

course Mth 151

¦çŹ’ô–Ózçeý˘Ĺ¶¶˙‹|ˇassignment #014

014. `query 14

College Algebra

05-15-2009

......!!!!!!!!...................................

10:38:01

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

......!!!!!!!!...................................

RESPONSE -->

If it is a picture then it tells a story (Book question)

confidence assessment: 3

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

......!!!!!!!!...................................

10:38:10

** 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. **

......!!!!!!!!...................................

RESPONSE -->

ok

self critique assessment: 3

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

......!!!!!!!!...................................

10:38:30

3.3.18 ~p false q false p -> q true

......!!!!!!!!...................................

RESPONSE -->

Right

confidence assessment: 3

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

......!!!!!!!!...................................

10:39:10

** 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. **

......!!!!!!!!...................................

RESPONSE -->

Ahh ok

self critique assessment: 3

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

......!!!!!!!!...................................

10:40:12

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

......!!!!!!!!...................................

RESPONSE -->

~b -> ~r ( out of the book)

confidence assessment: 3

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

......!!!!!!!!...................................

10:40:22

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

......!!!!!!!!...................................

RESPONSE -->

not what the question in the book is

self critique assessment: 3

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

......!!!!!!!!...................................

10:41:09

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

......!!!!!!!!...................................

RESPONSE -->

True *outof the book*

confidence assessment: 3

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

......!!!!!!!!...................................

10:41:18

** 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. **

......!!!!!!!!...................................

RESPONSE -->

not what is in the book

self critique assessment: 3

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

......!!!!!!!!...................................

10:47:33

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

......!!!!!!!!...................................

RESPONSE -->

P Q ( P^Q) (PVQ) (P^Q) -> (PVQ)

T T T T T

T F F T T

F T F T T

F F F F T

Tautology

confidence assessment: 2

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

......!!!!!!!!...................................

10:47:44

** 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. **

......!!!!!!!!...................................

RESPONSE -->

ok

self critique assessment: 3

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

......!!!!!!!!...................................

10:48:35

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

......!!!!!!!!...................................

RESPONSE -->

If you say I do then you will not be happy for the rest of your life (from the book)

confidence assessment: 3

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

......!!!!!!!!...................................

10:48:45

** 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). **

......!!!!!!!!...................................

RESPONSE -->

Not what is in the book)

self critique assessment: 3

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

......!!!!!!!!...................................

10:49:47

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

......!!!!!!!!...................................

RESPONSE -->

Because P and ~P cannot be the same at all times

confidence assessment: 3

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

......!!!!!!!!...................................

10:50:11

** 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. **

......!!!!!!!!...................................

RESPONSE -->

Basically I said that except I forgot to simplify it

self critique assessment: 3

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

&#Good responses. Let me know if you have questions. &#