Logic Flashcards
Study of Reasoning
LOGIC
Sentences or expressions that are not arbitrary but are the ones that are either true or false, but not both
PROPOSITIONS
Mathematical model that allows us to reason about truth and falsehood of logical expressions
PROPOSITIONAL LOGIC
Area of logic that deals with proposition. Developed by Greek philosopher, Aristotle
PROPOSITIONAL CALCULUS
The methods of producing new propositions from existing ones were discussed by English Mathematician ___________ in his book _________
GEORGE BOOLE, THE LAWS OF THOUGHT
Letters are used to denote ________ variables
PROPOSITIONAL VARIABLE
Are used to build complex or compound propositions from simpler ones
LOGICAL CONNECTIVES OR OPERATORS
A logical operator is that is applies to only a single proposition
UNARY
A logical operator that is applies to two propositions
BINARY
Give an example of unary operator
NEGATIION
A unary logical connective that takes the proposition p to another proposition which means not p
NEGATION OPERATOR
“It is not the case of P”
NEGATION OPERATOR
A binary logical connective that when applied to two propositions p and q, will yield “p and q”
CONJUNCTION
A binary logical connective that when a applied, will yield ‘p or q’
Disjunction
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
Inclusive OR
A proposition that is TRUE iF EXACTLY ONE OF P OR Q IS TRUE, BUT NOT BOTH.
Exclusive OR
A ___ or ___ operator is a binary logical connective that yields ‘if p then q’
CONDITIONAL OR IMPLICATION OPERATOR
In a conditional proposition, p is called the _____ (3 terms)
PREMISE, HYPOTHESIS, ANTECEDENT
In a conditional proposition, q is called the _____ (2 terms)
CONCLUSION or CONSEQUENT
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
p-> q
Is a condition that suffices to guarantee a particular outcome
SUFFICIENT CONDITION
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?)
SUFFICIENT CONDITION
A condition that is necessary for the particular outcome be achieved
NECESSARY CONDITION
p cannot be true unless q is true OR if q is false then p is false (WHAT CONDITION IS THIS)
NECESSARY CONDITION
~p -> ~q
INVERSE
q -> p
CONVERSE
~q -> ~p
CONTRAPOSITIVE
p if and only if q (give the two terms)
BICONDITIONAL OR MATERIAL EQUIVALENCE
for p and q to be trues, p and q should both be true or both false
BICONDITIONAL
the equivalent statement of biconditional operation is (in terms of p and q)
(p>q)A(q>p)
Represent relationship between the truth values of propositions and the formed compound propositions
TRUTH TABLES
List of all possible combinations and their corresponding output truth value once evaluated
TRUTH TABLE
formula for all possible values of combinations
n=2^k
Is composed of a sequence of statement called premise and concludion
ARGUMENT
A class of compound propositions that are ALWAYS TRUE for all possible combinations of truth values
TAUTOLOGY
is the opposite of tautology. it is a compound proposition that is always false (2 terms)
CONTRADICTION OR ABSURDITY
Compound values that have the same truth values in all possible combinations are called ____
LOGICALLY EQUIVALENT
Pertains to rules that can be used as building blocks to construct more complicated valid arguments
RULES OF INFERENCE
method of affirming (q)
modus ponens or law of detachment
p>r
Hypothethical syllogism
Method of denying ~p
Modus tollens
A valid argument that established the truth of a mathematical statement of the truth of a theorem
PROOF
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
Direct proof
to prove that p>q is true, it should be known that P IS FALSE. p>q is only true when p is false
VACUOUS PROOF
to prove that p>q is true, it should be known that Q IS true. p>q is only true when q is true
TRIVIAL PROOF
Puzzles that can be solved using logical reasoning
Logic puzzles
Are the basic building blocks of any digital dydtem
LOGIC GATES
Combination of propositions
Logical arguments
combinations of switches that control the flow of current
CIRCUITS
is an algebra that deals with binary variables and logical operations
BOOLEAN ALGEBRA
States that every algebraic expression deducible form the postulates of boolean algebra remains valid of the operators and identity elements are interchanged
DUALITY PRINCIPLE
______ have the property of creating any logic gate of any Boolean expression by combining them
universal gates
Give an example of universal gates
NOR and NAND
This refers to high value (1) 2 terms
NORMAL VARIABLE (PRIMED)
This refers to low value (0) 2 terms
INVERTIBLE (UNPRIMED)
