Home
Explore
Exams
Search for anything
Search for anything
Login
Get started
Home
OPTIMIZED LOGIC STUDY GUIDE (CH 2.2-3.4)
Studied by 2 people
0.0
(0)
Add a rating
View linked note
Learn
A personalized and smart learning plan
Practice Test
Take a test on your terms and definitions
Spaced Repetition
Scientifically backed study method
Matching Game
How quick can you match all your cards?
Flashcards
Study terms and definitions
1 / 44
There's no tags or description
Looks like no one added any tags here yet for you.
45 Terms
View all (45)
Star these 45
1
Conditional (p→q)
False only when p is true and q is false.
New cards
2
Truth table for p→q
Only false in the row where p is true and q is false.
New cards
3
Vacuously true
Occurs when the hypothesis p is false.
New cards
4
Key equivalence of p→q
p→q is equivalent to ~p∨q.
New cards
5
Negation of p→q
~(p→q) is equivalent to p∧~q.
New cards
6
Contrapositive
~q→~p, which is equivalent to the original conditional.
New cards
7
Converse
q→p, which is not equivalent to the original conditional.
New cards
8
Inverse
~p→~q, which is not equivalent to the original conditional.
New cards
9
Meaning of 'p only if q'
Represents the conditional p→q.
New cards
10
Biconditional (p↔q)
Defined as (p→q)∧(q→p).
New cards
11
Necessary condition
Saying 'You can't have p without q' means p→q.
New cards
12
Sufficient condition
Saying 'q automatically gives you p' means q→p.
New cards
13
Modus Ponens
If p→q and p are true, then q must be true.
New cards
14
Modus Tollens
If p→q and ~q are true, then ~p must be true.
New cards
15
Transitivity
If p→q and q→r are true, then p→r must be true.
New cards
16
Elimination
If p∨q and ~p are true, then q must be true.
New cards
17
Division into Cases
If p∨q, p→r, and q→r are true, then r must be true.
New cards
18
Contradiction Rule
If ~p leads to a contradiction, then p must be true.
New cards
19
Converse Error
The fallacy where p→q and q leads to the invalid conclusion of p.
New cards
20
Inverse Error
The fallacy where p→q and ~p leads to the invalid conclusion of ~q.
New cards
21
Predicate P(x)
A statement that contains variables.
New cards
22
Truth set
The set of values that make the predicate P(x) true.
New cards
23
Universal quantifier (∀x)
Indicates 'for all x'.
New cards
24
Existential quantifier (∃x)
Indicates 'there exists at least one x'.
New cards
25
Universal statement form
∀x, P(x) or ∀x, if P(x) then Q(x).
New cards
26
Negation of universal statements
~(∀x, P(x)) is equivalent to ∃x, ~P(x).
New cards
27
Negation of existential statements
~(∃x, P(x)) is equivalent to ∀x, ~P(x).
New cards
28
Negating Universal Conditional
~(∀x, P(x)→Q(x)) is equivalent to ∃x, P(x)∧~Q(x).
New cards
29
Order of quantifiers
The order matters: ∀x, ∃y, P(x,y) is not the same as ∃y, ∀x, P(x,y).
New cards
30
Negating multiple quantifiers
~(∀x, ∃y, P(x,y)) is equivalent to ∃x, ∀y, ~P(x,y).
New cards
31
Universal Instantiation
If ∀x, P(x) is true, then P(a) is true for any specific a.
New cards
32
Universal Modus Ponens
If ∀x, P(x)→Q(x) and P(a) are true, then Q(a) must be true.
New cards
33
Universal Modus Tollens
If ∀x, P(x)→Q(x) and ~Q(a), then ~P(a) must be true.
New cards
34
Venn diagram for 'All A are B'
Represented as A circle inside the B circle.
New cards
35
Venn diagram for 'No A are B'
Represented as non-overlapping circles.
New cards
36
'→' Symbol
Represents a conditional statement (if-then).
New cards
37
'↔' Symbol
Represents a biconditional statement (if and only if).
New cards
38
'∧' Symbol
Represents conjunction (and).
New cards
39
'∨' Symbol
Represents disjunction (or).
New cards
40
'~' Symbol
Represents negation (not).
New cards
41
'∀' Symbol
Represents the universal quantifier.
New cards
42
'∃' Symbol
Represents the existential quantifier.
New cards
43
'∈' Symbol
Represents 'element of'.
New cards
44
'∴' Symbol
Represents 'therefore'.
New cards
45
Operation order for logical expressions
Negation (~), followed by conjunction (∧) and disjunction (∨), then conditional (→) and biconditional (↔).
New cards
Explore top notes
Membranes- Chapter 3.1
Note
Studied by 20 people
894 days ago
5.0
(2)
Preview
🕳️
Biopsychology
Note
Studied by 1 person
50 days ago
5.0
(1)
Preview
PROCESS: Determining the Chemical (copy) (copy)
Note
Studied by 8 people
194 days ago
5.0
(1)
Preview
🌐
Chapter 9: Global Change
Note
Studied by 5562 people
707 days ago
5.0
(28)
Preview
🥼
Unit 1 notes LT 2: Lab Terms
Note
Studied by 21 people
904 days ago
5.0
(3)
Preview
🌎
Subjunctive
Note
Studied by 4 people
25 days ago
5.0
(1)
Preview
Biology Ch. 2
Note
Studied by 12 people
738 days ago
5.0
(1)
Preview
Chapter 6: Impacts of Linear Momentum
Note
Studied by 88 people
703 days ago
5.0
(2)
Preview
Explore top flashcards
Geo ( Metamorphic & Igneous)
Flashcard (49)
Studied by 21 people
370 days ago
5.0
(1)
Preview
Unit 1: Thinking Geographically - AP Outline
Flashcard (35)
Studied by 840 people
291 days ago
5.0
(1)
Preview
surface tension
Flashcard (48)
Studied by 1 person
61 days ago
5.0
(1)
Preview
I Vocab
Flashcard (20)
Studied by 10 people
710 days ago
5.0
(1)
Preview
Acqua Ragazza Menu Test
Flashcard (72)
Studied by 3 people
667 days ago
5.0
(1)
Preview
Chem: VSEPR & Polarity Test
Flashcard (26)
Studied by 58 people
357 days ago
5.0
(1)
Preview
Unit 1: Local community
Flashcard (38)
Studied by 3 people
226 days ago
5.0
(1)
Preview
Vocab. 251-300
Flashcard (50)
Studied by 86 people
675 days ago
5.0
(2)
Preview