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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
Q

Solve this:

P ^ ~P ≡

A

False

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26
Q

Solve this:

P v T ≡

A

True

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27
Q

Solve this:

P v F ≡

A

P

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28
Q

Solve this:

P ^ T ≡

A

P

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29
Q

Solve this:

P ^ F ≡

A

False

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30
Q

What is this law: (P v Q) ≡ Q v P

A

Commutative Law

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31
Q

What is this law: P v (Q v R) ≡ (P v Q) v R

A

Associative Law

32
Q

What is this law: P ^ (Q v R) ≡ (P ^ Q) v (P ^ R)

A

Distributive Law

33
Q

What is this law: ~(P v Q) ≡ ~P ^ ~Q

A

Demorgan’s Law

34
Q

What is the law: P -> Q ≡ ~P v Q

A

Equivalent to the Conditional

35
Q

What is the law: P Q ≡ (P -> Q) ^ (Q -> P)

A

Biconditional

36
Q

What is the law: (Q ^ P) ≡ P ^ Q

A

Commutative law

37
Q

What is the law: P ^ (Q ^ R) ≡ (P ^ Q) ^ R

A

Associative Law

38
Q

What is the law: P v (Q ^ R) ≡ (P v Q) ^ (P v R)

A

Distributive Law

39
Q

What is the law: ~(P ^ Q) ≡ ~P v ~Q

A

Demorgans law

40
Q

In related statements, what is the original equivalent to

A

The contrapositive

41
Q

(In related statements), what is p –> q called

A

Direct Statement

42
Q

(In related statements), what is q –> p called

A

Converse

43
Q

(In related statements), ~p –> ~q called

A

The inverse

44
Q

How do you take the inverse of something

A

You negate both sides

45
Q

(In related statements), ~q –> ~p called

A

Contrapositive

46
Q

How do you take the contrapositive of something

A

Turn it around and negate both

47
Q

When is p –> q = false

A

Only when p is true and q is false

48
Q

When is p–> q = true

A

Only when p is false or q is true

49
Q

What is step 1 of the transitive rule

A

Pick something that appears only once

50
Q

What is step 2 of the transitive rule

A

Start with ending “one” of last equation

51
Q

What is step 3 of the transitive rule

A

Pick the first and last value

52
Q

What is the equation of modus ponens

A

p —> q
p_____
∴ q

53
Q

What is the equation of modus tollens

A

p –> q
~q____
∴ ~p

54
Q

What is the equation of disjunctive sylloquism

A

p v q
~p___
∴ q

55
Q

What is the equation of transitive law

A

p –> q
q–>r
∴ p –> r

56
Q

What equation is this:
p —> q
p_____
∴ q

A

Modus ponens

57
Q

What equation is this:
p v q
~p___
∴ q

A

disjunctive sylloquism

58
Q

What equation is this:
p –> q
~q____
∴ ~p

A

modus tollens

59
Q

What equation is this:
p –> q
q–>r
∴ p –> r

A

transitive law

60
Q

What is a tip to memorize a TRUE logical property

A

There are 2 of them. Both use OR. One of the two has a NOT.

61
Q

What is a tip to memorize a FALSE logical property

A

There are 2 of them. Both use AND. One of the two has a NOT.

62
Q

What ia a tip to memorize a P logical property

A

There are 3 of them. One uses AND. One uses OR. The other uses NOT.

63
Q

What are some tips to memorize Demorgan’s Law

A

Contains NOT, (), P and Q

Two variations of the equation: OR x1 and AND x1

64
Q

What effect does using Demorgan’s Law have on a statement

A

You distribute the sign throughout the parenthesis

(removing the parenthesis in the process) and flip the sign

65
Q

What are some tips to memorize Communitative Laws

A

Contains (), P and Q

Two variations of the equation: OR x1 and AND x1

66
Q

What effect does using the Communitative law have on a statement

A

Rearranges the statement so P is in the first place and parenthesis are removed

67
Q

What are some tips to memorize Distributive Laws

A

Contains (), P, Q and R

68
Q

What is special about both variations of the distributive laws

A

Both contain a sign outside that is different from inside the parenthesis

69
Q

What are the signs in the first variation of the distributive law

A

and then (OR)

70
Q

What are the signs in the second variation of the distributive law

A

or then (AND)

71
Q

What effect does using the Distributive law have on a statement

A

Keep sign attached to P

outside the parenthesis) for inside the parenthesis. Then, inside sign goes inbetween the two () (

72
Q

What are some tips to memorize Associative laws

A

Contains (), P, Q and R.

Two variations: OR x1, AND x1

73
Q

What effect does using the Associative law have on a statement

A

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
Q

What are the tips to remember modus ponens

A

Contains p (implies) q
Second line is p
Therefore q

75
Q

What are tips to remember modus tollens

A

Contains p (implies) q
Second line is not q
Therefore ~p

76
Q

What are some tips to remember disjunctive sylloquism

A

Contains p (or) q.
Second line is ~p
Therefore q

77
Q

What is a tip to memorize transitive law

A 
Contains p (implies) q
Second line is q (implies) r
Therefor p (implies) r

Math (Comp. Sci) (5 decks)

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