Logic Flashcards

1
Q

Declarative sentence that can be true or false, but not both

A

Proposition

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2
Q

Proposition that conveys one thought only

A

Simple Proposition

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3
Q

Propositions that are put together using connective words

A

Compound Proposition

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4
Q

P ^ Q

A

Conjunction (and/but)

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5
Q

P → Q
P
———–
Q

A

Modus Ponens

If King is in checkmate, you’ve lost the game. King is in checkmate.
Therefore, you’ve lost the game.

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6
Q

P → Q
Q → R
———–
P → R

Hint: They all look synonymous to each other.

A

Law of Syllogism

If I study, I will get a good score in the exam.
If I get a good score in the exam, I will be happy. Therefore, If I study, I will be happy.

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7
Q

P V Q

A

Disjunction (or)

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8
Q

P -> Q

A

Conditional

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9
Q

P ⇔ Q

A

Biconditional

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10
Q

~ P

A

Negation

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11
Q

~ (~P)

A

Double Negation

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12
Q

P V 1 = 1
P ^ 0 = 0

A

Domination

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13
Q

P ^ 1 = P
P V 0 = P

Hint: The answer rhymes with P.

A

Identity

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14
Q

P V ~P = 1
P ^ ~P = 0

Hint: Kabaliktaran

A

Inverse/Excluded Middle

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15
Q

P V P = P
P ^ P = P

Hint: Same result, making it “strong”

A

Idempotent

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16
Q

P V Q = Q V P
P ^ Q = Q ^ P

Hint: Changed position, same concept

A

Commutative

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17
Q

~(P V Q) = ~P V ~Q
~(P ^ Q) = ~P ^ ~Q

A

De Morgan’s

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18
Q

P → Q = ~P V Q

Hint: “Pinalit” lang yung format ng pagsusulat

A

Switcheroo

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19
Q

P → Q = ~Q → ~P

Hint: Counters everything that the original statement had

A

Contrapositive

20
Q

P V (P ^ Q) = P
P ^ (P V Q) = P

A

Absorption

21
Q

P V (Q V R) = (P V Q) V R

A

Associative

22
Q

P V (Q ^ R) = (P V Q) ^ (P V R)

A

Distributive

23
Q

P

Hint: From mahaba to maiksi/isa nalang sya.

A

Simplification

If Harold is sleeping and Zoe is laughing,
then Harold is sleeping.

24
Q

P
Q
———
P ^ Q

Hint: Pinagsama

A

Conjunction

25
P --------- P V Q Hint: Dinagdagan
Addition If I am awake, then it is true that I am awake or I am hungry.
26
P → Q ~Q --------- ~P
Modus Tollens If Zeus is human, then Zeus is mortal. Zeus is not mortal. Therefore, Zeus is not human.
27
P → R Q → R --------- (P V Q) → R
Proof of Cases If Kim sleeps late, she will miss her flight. If Kim forgets something, she will miss her flight. Thus, if Kim sleeps late or forgets something, she will miss her flight.
28
~P → 0 --------- P
Contradiction It is false that I will not fail this subject. Therefore, I will fail this subject.
29
P V Q ~ P --------- Q Hint: Ano ulit tawag kapag may V symbol
Disjunctive Syllogism I will make tea or I will read a book. I will not make tea. Therefore, I will read a book.
30
P → Q Q --------- P
Fallacy of Converse If my alarm sounds, I will wake up. I woke up. Therefore, my alarm sounded. (Invalid)
31
P → Q --------- Q → P
Fallacy of Consequent If I water the plants, the plants grow. Therefore, if the plants grow, I water the plants. (Invalid)
32
P V Q P --------- ~Q
Affirming the Disjunct Alvin sings and dances with Nina. Alvin sings with Nina. Therefore, it is not true that Alvin dances with Nina.
33
P → Q ~P --------- ~Q
Fallacy of Inverse If today is Monday, then I have math class. Today is not Monday. Therefore, I do not have math class.
34
P → Q --------- ~P → ~Q
Improper Transposition
35
~ (P ^ Q) ~P --------- Q
Denying a Conjunct
36
37
Proposition that is always true
Tautology
38
Proposition that is always false
Contradiction
39
Proposition that is neither always true nor always false
Contingency
40
Converse of P → Q
Q → P
41
Inverse of P → Q
~P → ~Q
42
Contrapositive P → Q
~Q → ~P
43
44
45