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Math (Comp. Sci) > Logic Exam > Flashcards

Logic Exam Flashcards

Use logic to be logical

1
Q

What does the symbol “ ^ “ mean

A

AND

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2
Q

What does the symbol “ v “ mean

A

OR

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3
Q

What does the symbol “ ¬ “ mean

A

NOT

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4
Q

What does the symbol “ —-> “ mean

A

IMPLIES

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5
Q

What does the symbol “ “ mean

A

IMPLIES (BOTH WAYS)

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6
Q

What does the symbol “ ∴ “ mean

A

Therefor

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7
Q

What does the symbol “ ≡ “ mean

A

Equivalent to

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8
Q

What is the first priority of the truth table

A

Parenthesis

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9
Q

What is the second priority of the truth table

A

Nots

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10
Q

What is the third priority of the truth table

A

Ands

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11
Q

What is the fourth priority of the truth table

A

Ors

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12
Q

How would you approach filling the truth table values for P if there are only 2 variables:

A

P alternates every 2 values.

ex: T T F F

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13
Q

How would you approach filling the truth table values for Q if there are only 2 variables

A

Q alternates every 1 value

ex: T F T F

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14
Q

How would you approach filling the truth table values for p if there are 3 variables

A

P alternates every 4 values

ex: T T T T F F F F

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15
Q

How would you approach filling the truth table values for q if there are 3 variables

A

Q alternates every 2 values

ex: T T F F T T F F

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16
Q

How would you approach filling the truth table values for r if there are 3 variables

A

R alternates every 1 values

ex: T F T F T F T F

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17
Q

How would you approach solving proofs

A

Start with most complicated side first

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18
Q

What do you do if you see an “ Or “

A

If there is one thing thats true then it is all true

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19
Q

What do you do if you see an “ And “

A

If there is one thing that is false then it is all false

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20
Q

What is a tautology

A

A formula that is true in every interpretation

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21
Q

What does “ Ǝ “ mean

A

At least one (there exists)

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22
Q

What does “ ∀ “ mean

A

For all (everyone)

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23
Q

Solve this:

~(~P) ≡

A

P

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24
Q

Solve this:

P v ~P ≡

A

True

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25
Solve this: | P ^ ~P ≡
False
26
Solve this: | P v T ≡
True
27
Solve this: | P v F ≡
P
28
Solve this: | P ^ T ≡
P
29
Solve this: | P ^ F ≡
False
30
What is this law: (P v Q) ≡ Q v P
Commutative Law
31
What is this law: P v (Q v R) ≡ (P v Q) v R
Associative Law
32
What is this law: P ^ (Q v R) ≡ (P ^ Q) v (P ^ R)
Distributive Law
33
What is this law: ~(P v Q) ≡ ~P ^ ~Q
Demorgan's Law
34
What is the law: P -> Q ≡ ~P v Q
Equivalent to the Conditional
35
What is the law: P Q ≡ (P -> Q) ^ (Q -> P)
Biconditional
36
What is the law: (Q ^ P) ≡ P ^ Q
Commutative law
37
What is the law: P ^ (Q ^ R) ≡ (P ^ Q) ^ R
Associative Law
38
What is the law: P v (Q ^ R) ≡ (P v Q) ^ (P v R)
Distributive Law
39
What is the law: ~(P ^ Q) ≡ ~P v ~Q
Demorgans law
40
In related statements, what is the original equivalent to
The contrapositive
41
(In related statements), what is p --> q called
Direct Statement
42
(In related statements), what is q --> p called
Converse
43
(In related statements), ~p --> ~q called
The inverse
44
How do you take the inverse of something
You negate both sides
45
(In related statements), ~q --> ~p called
Contrapositive
46
How do you take the contrapositive of something
Turn it around and negate both
47
When is p --> q = false
Only when p is true and q is false
48
When is p--> q = true
Only when p is false or q is true
49
What is step 1 of the transitive rule
Pick something that appears only once
50
What is step 2 of the transitive rule
Start with ending "one" of last equation
51
What is step 3 of the transitive rule
Pick the first and last value
52
What is the equation of modus ponens
p ---> q p_____ ∴ q
53
What is the equation of modus tollens
p --> q ~q____ ∴ ~p
54
What is the equation of disjunctive sylloquism
p v q ~p___ ∴ q
55
What is the equation of transitive law
p --> q _q_-->_r_ ∴ p --> r
56
What equation is this: p ---> q p_____ ∴ q
Modus ponens
57
What equation is this: p v q ~p___ ∴ q
disjunctive sylloquism
58
What equation is this: p --> q ~q____ ∴ ~p
modus tollens
59
What equation is this: p --> q _q_-->_r_ ∴ p --> r
transitive law
60
What is a tip to memorize a TRUE logical property
There are 2 of them. Both use OR. One of the two has a NOT.
61
What is a tip to memorize a FALSE logical property
There are 2 of them. Both use AND. One of the two has a NOT.
62
What ia a tip to memorize a P logical property
There are 3 of them. One uses AND. One uses OR. The other uses NOT.
63
What are some tips to memorize Demorgan's Law
Contains NOT, (), P and Q | Two variations of the equation: OR x1 and AND x1
64
What effect does using Demorgan's Law have on a statement
You distribute the sign throughout the parenthesis | (removing the parenthesis in the process) and flip the sign
65
What are some tips to memorize Communitative Laws
Contains (), P and Q | Two variations of the equation: OR x1 and AND x1
66
What effect does using the Communitative law have on a statement
Rearranges the statement so P is in the first place and parenthesis are removed
67
What are some tips to memorize Distributive Laws
Contains (), P, Q and R
68
What is special about both variations of the distributive laws
Both contain a sign outside that is different from inside the parenthesis
69
What are the signs in the first variation of the distributive law
and then (OR)
70
What are the signs in the second variation of the distributive law
or then (AND)
71
What effect does using the Distributive law have on a statement
Keep sign attached to P | outside the parenthesis) for inside the parenthesis. Then, inside sign goes inbetween the two () (
72
What are some tips to memorize Associative laws
Contains (), P, Q and R. | Two variations: OR x1, AND x1
73
What effect does using the Associative law have on a statement
Remove P from outside bracket, put into first spot in bracket. Shift original first value to second bracket position. Original last value in bracket goes outside the parenthesis
74
What are the tips to remember modus ponens
Contains p (implies) q Second line is p Therefore q
75
What are tips to remember modus tollens
Contains p (implies) q Second line is not q Therefore ~p
76
What are some tips to remember disjunctive sylloquism
Contains p (or) q. Second line is ~p Therefore q
77
What is a tip to memorize transitive law
``` Contains p (implies) q Second line is q (implies) r Therefor p (implies) r ```

Math (Comp. Sci) (5 decks)

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