Propositional Logic 1 Flashcards
Logic is the science of…
reasoning.
_ reasoning and _ are based on the _ of logic.
Mathematical, arguments, rules
Reasoning is how we process…
our thinking in a logical way.
Logic contains…
propositions.
Propositions should be _ sentences, either _ or _.
declarative, true, false
Propositions cannot be _ or _ at the same time.
true, false
Propositions cannot be _ or _ at the same time.
true, false
Propositions cannot be 50%…
true or false.
Propositions cannot be a phrase or _.
onomatopoeia
Propositions should have a _ in equations.
quantifier
What is the foundation of logic?
Propositions.
These are letters that can represent propositions.
Propositional variables.
Compound propositions are combinations of…
1 or more propositions with logical connectives or operators.
These are also used in logic and computer languages.
Operators.
What is the symbol for negation?
”~” or “¬”.
A truth table is a tabular representation of all _ _ for _ and outputs.
value combinations, inputs
A truth table provides _ _ for results of applying an _ on each possible _ of _ _ for the operands.
truth values, operand, set, truth values
What are the symbols for conjunction?
“&”, “^”, or “*”.
A conjunction forms compound propositions with _ to join them.
“and”
_ can also be used in place of “and”.
“But”
A disjunction forms compound propositions with _ to join them.
“or”
What is the symbol for disjunction?
“v”.
“v” is called _.
“vel”
How does the precedence of operators go?
- ()
- ~
- v
- ⊕
- →
- ↔
Goes from left to right if the same operators are present.
An exclusive disjunction is also known as an exclusive _.
OR
What are the other ways to write ⊕?
- XOR
- EOR
- EXOR
- Direct sum
An exclusive disjunction can usually be _.
or
But not both.
What is the rule in exclusive disjunction?
Compound propositions are true if one is true. Otherwise, false.
“If p then q” is a _ statement.
conditional
In a conditional statement, the p can be denoted as…
premise, hypothesis, and antecedent.
In a conditional statement, the q can be denoted as…
conclusion, and consequent.
What is the rule in conditional statements?
All compond propositions are true except when true implies false.
In constructing a truth table, the amount of rows increase _ as more propositions are added.
exponentially
n proposition = 2^n rows.
How is p↔q read?
“p if and only if p”.
Biconditional statements are called…
bi-implication, or biconditional of p and q.
Biconditionality is also known as…
logical equality.
What is the rule in biconditionality?
Compound propositions are true if both are the same. Otherwise, false.
Tautology is an always…
true logical expression.
Contradictions are also known as…
fallacies, or unsatisfiable.
Contradictions are always…
false.
What is a contingency?
It is neither a tautology nor a contradiction.
