Logic

Question 1

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

Answer 1

Proposition

Question 2

Proposition that conveys one thought only

Answer 2

Simple Proposition

Question 3

Propositions that are put together using connective words

Answer 3

Compound Proposition

Question 4

P ^ Q

Answer 4

Conjunction (and/but)

Question 5

P → Q
P
———–
Q

Answer 5

Modus Ponens

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

Question 6

P → Q
Q → R
———–
P → R

Hint: They all look synonymous to each other.

Answer 6

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.

Question 7

P V Q

Answer 7

Disjunction (or)

Question 8

P -> Q

Answer 8

Conditional

Question 9

P ⇔ Q

Answer 9

Biconditional

Question 10

~ P

Answer 10

Negation

Question 11

~ (~P)

Answer 11

Double Negation

Question 12

P V 1 = 1
P ^ 0 = 0

Answer 12

Domination

Question 13

P ^ 1 = P
P V 0 = P

Hint: The answer rhymes with P.

Answer 13

Identity

Question 14

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

Hint: Kabaliktaran

Answer 14

Inverse/Excluded Middle

Question 15

P V P = P
P ^ P = P

Hint: Same result, making it “strong”

Answer 15

Idempotent

Question 16

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

Hint: Changed position, same concept

Answer 16

Commutative

Question 17

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

Answer 17

De Morgan’s

Question 18

P → Q = ~P V Q

Hint: “Pinalit” lang yung format ng pagsusulat

Answer 18

Switcheroo

Question 19

P → Q = ~Q → ~P

Hint: Counters everything that the original statement had

Answer 19

Contrapositive

Question 20

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

Answer 20

Absorption

Question 21

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

Answer 21

Associative

Question 22

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

Answer 22

Distributive

Question 23

P

Hint: From mahaba to maiksi/isa nalang sya.

Answer 23

Simplification

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

Question 24

P
Q
———
P ^ Q

Hint: Pinagsama

Answer 24

Conjunction

Question 25

P V Q

Hint: Dinagdagan

Answer 25

Addition

If I am awake,
then it is true that I am awake or I am hungry.

Question 26

P → Q
~Q
———
~P

Answer 26

Modus Tollens

If Zeus is human, then Zeus is mortal.
Zeus is not mortal.
Therefore, Zeus is not human.

Question 27

P → R
Q → R
———
(P V Q) → R

Answer 27

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.

Question 28

P

Answer 28

Contradiction

It is false that I will not fail this subject.
Therefore, I will fail this subject.

Question 29

P V Q
~ P
———
Q

Hint: Ano ulit tawag kapag may V symbol

Answer 29

Disjunctive Syllogism

I will make tea or I will read a book.
I will not make tea.
Therefore, I will read a book.

Question 30

P → Q
Q
———
P

Answer 30

Fallacy of Converse

If my alarm sounds, I will wake up.
I woke up.
Therefore, my alarm sounded. (Invalid)

Question 31

Q → P

Answer 31

Fallacy of Consequent

If I water the plants, the plants grow.
Therefore, if the plants grow, I water the plants. (Invalid)

Question 32

P V Q
P
———
~Q

Answer 32

Affirming the Disjunct

Alvin sings and dances with Nina.
Alvin sings with Nina.
Therefore, it is not true that Alvin dances with Nina.

Question 33

P → Q
~P
———
~Q

Answer 33

Fallacy of Inverse

If today is Monday, then I have math class.
Today is not Monday.
Therefore, I do not have math class.

Question 34

~P → ~Q

Answer 34

Improper Transposition

Question 35

~ (P ^ Q)
~P
———
Q

Answer 35

Denying a Conjunct

Question 37

Proposition that is always true

Answer 37

Tautology

Question 38

Proposition that is always false

Answer 38

Contradiction

Question 39

Proposition that is neither always true nor always false

Answer 39

Contingency

Question 40

Converse of P → Q

Answer 40

Q → P

Question 41

Inverse of P → Q

Answer 41

~P → ~Q

Question 42

Contrapositive P → Q

Answer 42

~Q → ~P