Chap 7 ( up until 260)

Question 1

why should we worry about logical structure?

Answer 1

(1) Comprehension: Helps us to better see the underlying forms of argument.

(2) Positive Evaluation: Helps us to readily spot (and create) valid arguments.

(3) Negative Evaluation: Helps us to readily spot (and avoid creating) invalid arguments.

Question 2

whats a Simple Statement

Answer 2

Contains no other statement as a component part. (We represent it with a letter, like “P”.)

Question 3

whats a Complex Statement?

Answer 3

Contains at least one other statement as a component part.

Question 4

whats a Logical Operator?

Answer 4

Special expressions which work to combine simple statements into complex ones: AND, OR, IF…THEN, NOT

1) Conjunction
2) Negation
3) Disjunction
4) Conditional

Question 5

whats a Conjunction ?

Answer 5

• a Logical Operator
• two simple sentences joined by a connective to form a compound statement
• “and”

Question 6

if one or both of the conjuncts is false then the sentence is….

Answer 6

false

Question 7

whats the symbol for conjunctions?

Answer 7

& ( ampersand)

Question 8

Other conjunct. words:

Answer 8

‘however’, ‘although’, ‘nonetheless’, ‘moreover’.

Question 9

Give an example of a conjunction.

Answer 9

• Alice is happy AND Jim is sad
• Justin Trudeau is Prime Minister now, but Tom Mulcair will be soon.
• The lecture was poorly-presented, even though the topic was interesting.
• John had cake and Jill had pie.

Question 10

whats a Disjunction?

Answer 10

• a logical operator
• coumpound statemnet of the form “either p or Q”.
• p v q
• A disjunctions is true even if only one disjunctions is true and false only if both disjunctions are false

Question 11

When is a disjunction true?

Answer 11

• A disjunctions is true even if only one disjunctions is true

Question 12

When is a disjunction fasle ?

Answer 12

if both disjunctions are false

Question 13

whats the symbol for disjunstions

Answer 13

V ( wedge)

Question 14

Other disjunct. words:

Answer 14

English: ‘exclusive’ sense. “A v B, and not both.”
Logic: ‘inclusive’ sense.

Question 15

examples of disjunctions

Answer 15

• “Either John had cake or Jill had pie.”
• Alice is happy OR Jim is sad

Question 16

whats Negation?

Answer 16

• logical operator
• denial of a statement which we indicate
• “not”
• ~p

Question 17

Other expressions include negation

Answer 17

Other expressions include: ‘it’s not true that’; ‘it’s false that’; ‘it’s not the case that’.

Question 18

symbol negation

Answer 18

~ ( tilde)

Question 19

when can a negation be false? .

Answer 19

False if and only if p is true.

Question 20

whats an antecedent?

Answer 20

first part of a conditional statemmt ( if p then q) , the part that begins with “if”

Question 21

whats a consequent

Answer 21

The end part of a conditional statement
- introduced by the term “then:

Question 22

whats Conditional?

Answer 22

if - then statement
p → q

Question 23

symbol for conditional

Answer 23

→ (arrow)

Question 24

when is a conditionla sentence false

Answer 24

False if and only if the antecedent is true AND the consequent is false.

Question 25

examples of conditional sentences

Answer 25

• If John had cake, then Jill had pie
  examples with no if then temrs but follow the format:
  “Since your lease expired the landlord is free to raise the rent”

“Being a teenager means you have lots of problems”

“Anyone who likes logic is a fool”

“The truth of evolution implies the falsity of the Bible”

“Whenever Lebowski drinks coffee, he gets antsy”

Question 26

Tricky Point About Conditionals: “If” vs “Only If”

Answer 26

The word “if”, by itself, introduces the antecedent, no matter where it occurs in a statement.

	“If I skip class, I’ll find the material difficult”
	“I’ll find the material difficult if I skip class.
	These are equivalent, and should be written as: S 🡪 D

The expression “only if” introduces the consequent, no matter where it occurs in a statement.
“Only if the price drops will I buy the giant TV”
“I will buy the giant TV only if the price drops”
These are equivalent, and should be written as: B 🡪 P

Question 27

Tricky Point: Combining Logical Operators

Answer 27

A logical operation can be performed on a compound statement:

     Both Tim and Sue will win the award.	
		T  &   S
     It’s not the case that both Tim and Sue will win the award.
		~ (T & S)

Just like in math, it matters where you put the brackets: the sentence above is not equivalent to ~T & S

Similarly, there’s an important difference between these two:

     R → (W & M)	     If it rains, I am wet and miserable.
   	    (R → W)  &  M	     If it rains, I am wet. And I’m miserable

Question 28

Combining Conjunction and Disjunction With Negation

Answer 28

Consider a conjunction, which is then negated:

Both Tim and Sue will graduate. (T & S)
It’s not the case that both Tim and Sue will graduate. ~ (T & S)

  This is not equivalent to   ~T & ~S         Why?    But it is equivalent to       ~T v ~S         Why?

Next, consider a negated disjunction: ~(T v S)
This reads: It’s not the case that either Tim or Sue will graduate.

This is not equivalent to ~T v ~S Why?
This is equivalent to ~T & ~S Why?