Propositional Logic

Question 1

T ^ T =
T ^ F =
F ^ T =
F ^ F =

Answer 1

T
F
F
F

Question 2

Logical equivalency

Answer 2

Two propositions, say P and Q, are logically equivalent if P ⟺ Q is a TAUTOLOGY. In this case, the biconditional of P and Q (i.e. P ⟺ Q) is called a logical equivalency.

Question 3

What is the no. of rows in a truth table for 3 propositions?

Answer 3

2^3 = 8

Question 4

Premise

Answer 4

Proposition (atomic/compound) to the left of the implication operator. Also called antecedent or hypothesis.

Question 5

Exclusive-Or

Answer 5

A compound proposition where ONLY the “XOR” operator is applied on 2 or more propositions.

Question 6

Commutative properties (logical equivalencies)

Answer 6

P v Q ⟺ Q v P
P ^ Q ⟺ Q ^ P

Question 7

Implication Law

Answer 7

(P ⇒ Q) ⟺ (¬P v Q)

Question 8

Consequence

Answer 8

Proposition (atomic/compound) to the right of the implication operator. Also called conclusion.

Question 9

Contingency

Answer 9

A compound proposition (statement) that is NEITHER a TAUTOLOGY NOR a CONTRADICTION.

Question 10

Which words does conjunction (^) denote?

Answer 10

“and”, “but”, “also”, “as well as”

Question 11

How is an implication of 2 statements/propositions, say P and Q written in English, where P ⇒ Q?

Answer 11

“if P then Q”
“If P, Q”
“P implies Q”
“Whenever P, Q”
“P is sufficient for Q”
“Q is necessary for P”
“Not P unless Q”
“P only if Q”
“Q if P”
“Q whenever P”

Question 12

T ⇒ T
T ⇒ F
F ⇒ T
F ⇒ F

Answer 12

T
F
T
T

Question 13

What is the no. of rows in a truth table for an n no. of propositions?

Answer 13

2^n

Question 14

Negation operator

Answer 14

¬ or ~

Question 15

Biconditional of P and Q

Answer 15

A compound proposition which is TRUE precisely when either P and Q are BOTH TRUE, or when P and Q are BOTH FALSE.

Question 16

Implication

Answer 16

A compound proposition where ONLY the “IMPLIES/IF-THEN” (conditional) operator is applied on 2 propositions.

Question 17

Conjunction

Answer 17

A compound proposition where ONLY the “AND” operator is applied on 2 or more propositions.

Question 18

Biconditional symbol

Answer 18

↔ or ⟺

Question 19

Conjunction symbol

Answer 19

(^)

Question 20

Conclusion

Answer 20

Proposition (atomic/compound) to the right of the implication operator. Also called consequence.

Question 21

Difference between disjunction/OR/v and or-exclusive/XOR/⊕ ?

Answer 21

In a disjunction of 2 statements, the truth value is “true” if both statements are true, but an exclusive-or of 2 statements is false if both statements are true.

Question 22

truth value

Answer 22

The value of a proposition; it can be either “true” or “false”

Question 23

Logical equivalency between Implication and Contrapositive

Answer 23

(P ⇒ Q) ⟺ (¬Q ⇒ ¬P)

Question 24

T ⊕ T =
T ⊕ F =
F ⊕ T =
F ⊕ F =

Answer 24

F
T
T
F

Question 25

DeMorgan's Laws (logical equivalencies)

Answer 25

¬(P ^ Q) ⟺ ¬P v ¬Q ¬(P v Q) ⟺ ¬P ^ ¬Q

Question 26

Tautology

Answer 26

A compound proposition (statement) that is ALWAYS TRUE IRRESPECTIVE of the TRUTH VALUES of the propositions in it.

Question 27

compound proposition

Answer 27

A proposition that is a combination of two or more propositions through logical operators such as "and", "or", "not", etc.

Question 28

Order of operations (highest to lowest precedence)

Answer 28

Negation, Conjunction, Disjunction, Exclusive-or, Implication, Biconditional

Question 29

Disjunction symbol

Answer 29

V

Question 30

Associative properties (logical equivalencies)

Answer 30

(P v Q) v R ⟺ P v (Q v R) (P ^ Q) ^ R ⟺ P ^ (Q ^ R)

Question 31

What is the no. of rows in a truth table for 4 propositions?

Answer 31

2^4 = 16

Question 32

proposition

Answer 32

A statement that can only be either true or false.

Question 33

~T --> ~F -->

Answer 33

F T

Question 34

T v T = T v F = F v T = F v F =

Answer 34

T T T F

Question 35

Converse of P ⇒ Q

Answer 35

Q ⇒ P

Question 36

How is a biconditional of 2 statements/propositions, say P and Q written in English?

Answer 36

"P if and only if Q", "Q if and only if P", "P iff Q", "Q iff P", "P is necessary and sufficient for Q", "Q is necessary and sufficient for P", "if P then Q, and conversely", "if Q then P, and conversely".

Question 37

Truth Table

Answer 37

A table that displays the possible values for a proposition or propositions as well as the results which followed when operators are applied.

Question 38

Inverse of P ⇒ Q

Answer 38

¬P ⇒ ¬Q

Question 39

Implication symbol

Answer 39

⇒ or →

Question 40

Contrapositive of P ⇒ Q

Answer 40

¬Q ⇒ ¬P

Question 41

How is a biconditional of 2 statements/propositions, say P and Q written in English?

Answer 41

"P if and only if Q", "Q if and only if P", "P iff Q", "Q iff P", "P is necessary and sufficient for Q", "Q is necessary and sufficient for P", "if P then Q, and conversely", "if Q then P, and conversely".

Question 42

Exclusive-Or symbol

Answer 42

⊕

Question 43

Antecedent

Answer 43

Proposition (atomic/compound) to the left of the implication operator. Also called premise or hypothesis.

Question 44

Hypothesis

Answer 44

Proposition (atomic/compound) to the left of the implication operator. Also called premise or antecedent.

Question 45

Distributive properties (logical equivalencies)

Answer 45

P v (Q ^ R) ⟺ (P v Q) ^ (P v R) P ^ (Q v R) ⟺ (P ^ Q) v (P ^ R)

Question 46

Double negation property (a logical equivalency)

Answer 46

¬ (¬ P) ⟺ P is a tautology.

Question 47

Contradiction

Answer 47

A compound proposition (statement) that is ALWAYS FALSE IRRESPECTIVE of the TRUTH VALUES of the propositions in it.

Question 48

Logical equivalency between Inverse and Converse

Answer 48

(Q ⇒ P) ⟺ (¬P ⇒ ¬Q)

Question 49

T ⟺ T T ⟺ F F ⟺ T F ⟺ F

Answer 49

T F F T

Question 50

Disjunction

Answer 50

A compound proposition where ONLY the "OR" operator is applied on 2 or more propositions.