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Discrete Mathematics > Logic > Flashcards

Logic Flashcards

1
Q

Study of Reasoning

A

LOGIC

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2
Q

Sentences or expressions that are not arbitrary but are the ones that are either true or false, but not both

A

PROPOSITIONS

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3
Q

Mathematical model that allows us to reason about truth and falsehood of logical expressions

A

PROPOSITIONAL LOGIC

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4
Q

Area of logic that deals with proposition. Developed by Greek philosopher, Aristotle

A

PROPOSITIONAL CALCULUS

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5
Q

The methods of producing new propositions from existing ones were discussed by English Mathematician ___________ in his book _________

A

GEORGE BOOLE, THE LAWS OF THOUGHT

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6
Q

Letters are used to denote ________ variables

A

PROPOSITIONAL VARIABLE

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7
Q

Are used to build complex or compound propositions from simpler ones

A

LOGICAL CONNECTIVES OR OPERATORS

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8
Q

A logical operator is that is applies to only a single proposition

A

UNARY

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9
Q

A logical operator that is applies to two propositions

A

BINARY

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10
Q

Give an example of unary operator

A

NEGATIION

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11
Q

A unary logical connective that takes the proposition p to another proposition which means not p

A

NEGATION OPERATOR

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12
Q

“It is not the case of P”

A

NEGATION OPERATOR

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13
Q

A binary logical connective that when applied to two propositions p and q, will yield “p and q”

A

CONJUNCTION

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14
Q

A binary logical connective that when a applied, will yield ‘p or q’

A

Disjunction

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15
Q

the disjunction pVq is the proposition that is true when EITHER P IS TRUE, Q IS TRUE, OR BOTH ARE TRUE, AND FALSE OTHERWISE is called

A

Inclusive OR

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16
Q

A proposition that is TRUE iF EXACTLY ONE OF P OR Q IS TRUE, BUT NOT BOTH.

A

Exclusive OR

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17
Q

A ___ or ___ operator is a binary logical connective that yields ‘if p then q’

A

CONDITIONAL OR IMPLICATION OPERATOR

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18
Q

In a conditional proposition, p is called the _____ (3 terms)

A

PREMISE, HYPOTHESIS, ANTECEDENT

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19
Q

In a conditional proposition, q is called the _____ (2 terms)

A

CONCLUSION or CONSEQUENT

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20
Q

The implication ____ is the proposition that is false precisely when p is true but q is false. MEANING IF THE PREMISE IS SATISFIES THAN IT FOLLOWS THAT THE CONCLUSION SHOULD HAPPEN

A

p-> q

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21
Q

Is a condition that suffices to guarantee a particular outcome

A

SUFFICIENT CONDITION

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22
Q

If the condition does not hold, the outcome might be achieved in another way OR if the condition does hold, the outcome is guaranteed (WHAT CONDITION IS THIS?)

A

SUFFICIENT CONDITION

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23
Q

A condition that is necessary for the particular outcome be achieved

A

NECESSARY CONDITION

24
Q

p cannot be true unless q is true OR if q is false then p is false (WHAT CONDITION IS THIS)

A

NECESSARY CONDITION

25
Q

~p -> ~q

A

INVERSE

26
Q

q -> p

A

CONVERSE

27
Q

~q -> ~p

A

CONTRAPOSITIVE

28
Q

p if and only if q (give the two terms)

A

BICONDITIONAL OR MATERIAL EQUIVALENCE

29
Q

for p and q to be trues, p and q should both be true or both false

A

BICONDITIONAL

30
Q

the equivalent statement of biconditional operation is (in terms of p and q)

A

(p>q)A(q>p)

31
Q

Represent relationship between the truth values of propositions and the formed compound propositions

A

TRUTH TABLES

32
Q

List of all possible combinations and their corresponding output truth value once evaluated

A

TRUTH TABLE

33
Q

formula for all possible values of combinations

A

n=2^k

34
Q

Is composed of a sequence of statement called premise and concludion

A

ARGUMENT

35
Q

A class of compound propositions that are ALWAYS TRUE for all possible combinations of truth values

A

TAUTOLOGY

36
Q

is the opposite of tautology. it is a compound proposition that is always false (2 terms)

A

CONTRADICTION OR ABSURDITY

37
Q

Compound values that have the same truth values in all possible combinations are called ____

A

LOGICALLY EQUIVALENT

38
Q

Pertains to rules that can be used as building blocks to construct more complicated valid arguments

A

RULES OF INFERENCE

39
Q

method of affirming (q)

A

modus ponens or law of detachment

40
Q

p>r

A

Hypothethical syllogism

41
Q

Method of denying ~p

A

Modus tollens

42
Q

A valid argument that established the truth of a mathematical statement of the truth of a theorem

A

PROOF

43
Q

shows that a conditional statement p>q is true by showing that IF P IS TRUE, THEN Q MUST ALSO BE TRUE. the combination of p is true and q is false never occurs

A

Direct proof

44
Q

to prove that p>q is true, it should be known that P IS FALSE. p>q is only true when p is false

A

VACUOUS PROOF

45
Q

to prove that p>q is true, it should be known that Q IS true. p>q is only true when q is true

A

TRIVIAL PROOF

46
Q

Puzzles that can be solved using logical reasoning

A

Logic puzzles

47
Q

Are the basic building blocks of any digital dydtem

A

LOGIC GATES

48
Q

Combination of propositions

A

Logical arguments

49
Q

combinations of switches that control the flow of current

A

CIRCUITS

50
Q

is an algebra that deals with binary variables and logical operations

A

BOOLEAN ALGEBRA

51
Q

States that every algebraic expression deducible form the postulates of boolean algebra remains valid of the operators and identity elements are interchanged

A

DUALITY PRINCIPLE

52
Q

______ have the property of creating any logic gate of any Boolean expression by combining them

A

universal gates

53
Q

Give an example of universal gates

A

NOR and NAND

54
Q

This refers to high value (1) 2 terms

A

NORMAL VARIABLE (PRIMED)

55
Q

This refers to low value (0) 2 terms

A

INVERTIBLE (UNPRIMED)

Discrete Mathematics (5 decks)

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