Class notes

GNED 1101 study notes

255 views 2 purchases

Institution
Mount Royal University (MRU )

Book
GNED 1101 MRU

The notes are written by asking related questions surrounding the learning objectives for this course. Between the brackets is the answer to the question. Use the adjacent cells of the document to determine if you understand the concept. Color the cells red if you can't recall the information. Yell...

[Show more]

Preview 4 out of 46 pages

View example

Uploaded on January 2, 2021
Number of pages 46
Written in 2020/2021
Type Class notes
Professor(s) Monique horbay
Contains All classes

gned 1101
mount royal university
mru
scientific and mathematical literacy
dr monique horbay

CA$10.92

Added

Add to cart Add to wishlist

100% satisfaction guarantee
Immediately available after payment
Both online and in PDF
No strings attached

Section 1 Statements, Negations, Conjunction and Quantified statements
1.Identify english sentences that are statements
2.Express statements using symbols
3.Form the negation of a statement
4. Express negations using symbols
5.Translate a negation represented by symbols into english
6. Express quantified statments in two ways
7. Write negations of wuantified statements

1.what is a statement ( is a sentence either true or false )
what is not a statement ( opinion, questions, exclamations, order)
what symbol do we use for a statement ( p, q, r, s )
2.what is a negation ( the opposite of the given statement )
what words can we use to negate a statement ( it is not true )
symbol for negate statement ( ~p )
what does ~p mean ( "not p" or " it is not true that p." )
translating a symbolic stamement into words ~p ( it is not true that p )
3. What is a Quantified statement ( a statement containing all, some, and none )
what are the quatified statements ( All "A" are "B", Some "A" are B", No "A" are "B", Some "A" are not "B" )
the eq of All "A" are "B" ( there is not one A that is not B )
the eq of Some "A" are B ( there exist one A that is B )
the eq of No "A" are "B" ( All A are not B )
the eq of Some "A" are not "B" ( not all A are B )
4. Negation of a quantified statement All "A" are "B" ( Some A are not B )
Negation of No "A" are "B" ( Some A are B )

Section two Compound Statements
1. Express the compound statement in symbolic form
2.Express symbolic statements with parentheses in english
3. Use the dominance connectives

1.What is a compound statement ( statements form from combining two or more simple statments )
what are connectives used in a compound statement ( and, or, if, and if and only if )

AND STATMENTS
what is a conjuction ( compound statements formed by connecting statements with the word "and" )
what is the symbol for and ( ^ )
what i the symbolic form of statements it is 5pm they are working and it is 5pm they are not working ( p ^ q and
what are other connectives ( but, yet, nevertheless )
what i a conjunction ( can be broken down into two sentences )
example ( beer and pizza are not rec for people with uclers 1. pizza is not rec for people w/ulcers 2. beer " "

,OR STATMENTS
what is an exclusive or ( " one or the other but not both" )
what is an inclusive or ( " one or the other or both" )
what or is used in mathematics ( inclusive )
what is used in two simple sentences rep by p or q ( p or q or both )
what is a nondisjunction ( compound statments by connecting simple statements by the word or )
how is non disjuction represented ( V )
IF THEN STATEMENTS
what is aa conditional statements ( connecting simple statements with "if then " )
what is if statment ( if q then p )
what is the symbol ( -> )
what is the antecedent ( the statment before the connective or the symbol )
what is the codequent ( the statment after the connective )
what is conditional ( one direction )
what is Biconditional ( two way )
what are the common english expression for bi conditional
p if and only if q
q if and only if p
if p then q, and if q then p
p is nesceceasry and suffienct for q
q is nesscesart and suffient for p

q is nescessary for p ( the symoblic for would be p -> q the statment after the word nesccessary is the antecede
q is suffient for p ( the symbolic form woubd be q -> p the the statement before suffient is the atecendent )
SYMBOLIC STATEMENTS WITH PARAENTHESIS
what the parentheses mean ( either negation of entire sentence p q, or to indicate a comma in groupings )
~ ( p ^ q ) ( negation of entire sentence )
when expressesd in english paretheses are view ( a comma to indicate groupings )
How is a statment determine from compound statements containting more then one connecrtive ( the one outsid
where is the comma placed in compound statements containing more than one connective ( the simple statmen
DOMINANCE OF CONNECTIVES
If a symbolic statements appears without parentheses ( statements before and after the most dominant connec
what is the order of dominance ( Biconditionl > Conditional > Conjuction/Disjunction > Negation )
Clinton Lew
When expressesd in english paretheses are view ( a comma to indicate groupings )
When am I supposed to use the dominance of connectives ( if grouping symbols are not given in compound sym

Section 3 Truth tables for Negation, Conjuction, and Disjunction
classifying a true statment is called ( assigning a truth value to the statement )
the negation of a false statment is ( true )
the negation of a true statment is ( false )

,if both statements are true then the compound statement is ( true )
if one statement is false then the compound statement is ( false )
if both statments is false then the compond statment is ( true)
when is a conjunction false ( when both statments are either or )
what are component statements ( statements making up a compound statement )
what are the truth tables for non disjunction ( when a component statement is true the compound statem
when is a conjuntion false ( when both component statements are false then the compond statement is
negation of a compound statment ( either not or not true )

~p ^ q ( not p and q )

CONSTRUCTING TRUTH TABLES FOR COMPOUND STATEMENT CONTAINING ONLY THE SIMPLE STAT
what is filled in first ( component statements )
if a coloum heading involes negtion ( determine by taking the opposite of the coloum containing component sta
if a coloum heading involes conjunction ( determine from component statements it is only true when both statem
if a coloum heading involes non disjunction ( determine from component statments it is false when both stateme
What is TAUTOLOGY ( a compound statement that is always true )
CONSTRUCTING A TRUTH TABLE WITH EIGHT CASES
what are the 8 cases of p q and r ( 4 true, 4 False, tt -> ff, tf )
when is the conjuntion true with 3 statements ( when p and q are true )

Section 4 Constructing truth tables for the conditional and the Biconditional
1. Understand the logic behind the definition of the conditional
2. Contruct truth tables for the conditional statement
3.Understand the definition of the biconditional
4.Construct truth tables for biconditional statements
5.Determine the truth value of a compound statement for specific case

what is the definition of the conditional ( a conditional is false only when the antcedent is true and the co
what is a biconditional ( true when the compent statement have the same truth value )

Section 5 Equivalent Statments and variations of Conditional statements
1. Use a truth table to show that statements are equivalent
2. Wrtie the contrapositive for a conditional statement
3. Write the converse and inverse of a conditional statement

EQUIVALENT STATEMENT ( are made up of the same simple statements and have the same corresponding tru
what is p v ~q equivalent to ( ~p -> ~q )
the bill recieves marjority approval or the bill does not becomes the law eq to ( If the bill does not receieve marjo
what is p v q eq to ( ~q -> p, or ~p -> q, or q V p )
what is the symbol to show that statements are equivalent ( addidas sign three strips )

, Double negation of a statement is the eq of ( the statement )
what is an example of doube negation ( we can't not pay bills that weve already incurred = we can pay bills that
when given multiple statment to determine eq ( build a truth table base on the statement then compare with orgi
VARIATION OF A CONDITIONAL STATEMENT
the truth value of a condition stetement does not change when ( the the acedent and coseqdent is reversed and

what i a contrapositive of a conditional statement ( obtained by reversing the negated form of the antecedent an
what is a converse ( if the antecedent and cosequent is inverse but not negated )
what is a inverse ( is the antecedent and cosequent is negated but not inversed )
the relationship among the inverse and converse is ( they have the same truth values )

section 6 Negation of conditional statements and de morgans law
1. Wrtie the negation of a conditional statement
2. Use de morgans law

how to write the negation of a conditional statement symboliy p -> q ( negate the cosequent and change the con
what is de morgans law in word ( conjuntion = a disjuntion vice versa )
De morgans law symoblicly ( ~ ( p ^ q ) = ( ~p V ~q ) and ~ ( p V q ) = ~p ^ ~q and ~ ( p -> q) = p ^ ~q

Using morgans law how do you negate a conjuuntion ( negate each component and change and to or )
using morgans law how do you negate a disjuntion ( negate each compoenent and change or to and )
Using De morgans law to formulate a contrapositive
write a statement that is eq to if it rains, I do not go outside and I study ( use contrapositive and use de morgans
Section 7 Arguments and Truth Values
1. Use truth Values to determine Validity
2. Recognize and use forms of valid and invalid arguments

what does an argument consist of ( the premises and conclusion )
what is premises ( the given statements )
when is an argument valid ( if the conclusion is true when ever the premises are assumed to be true )
an argument that is not valid is said to be ( invalid argument or called a fallacy )
HOW TO WRITE THE PREMISES AND CONCLUSION IN SYMBOLIC FORM
Premise 1: if children murder their parents in cold blood, they deserve to be punished to the full extent of the law
Premise 2: These children murder their parent in cold blood ( p )
Conclusion: Therefore these chlidren deserve to be punished to the full extent of the law ( therfore q )
how do you write this conditional ( (p->q) ^ p ) -> q
what does ( (p->q) ^ p ) -> q break down to ( if premise 1 ( p-> q ) and premise 2 then conclusion )
how to determine a valid argument ( if the truth table is a tautology )
what is direct reasoning ( take the form of p->q, p, therefore q which are always valid arguments )
TESTING THE VALIDITY OF AN ARGUMENT WITH A TRUTH TABLE
1. Use letter to rep statements

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller romcrpz. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for CA$10.92. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

59325 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling

Class notes

GNED 1101 study notes

Document information

Subjects

Connected book

More summaries for

Written for

Seller

Content preview