Logic Flashcards
logic
the study of formal reasoning
proposition
a statement that is either true or false, typically declarative sentences
truth value
indicating whether the proposition is actually true or false
compound proposition
created by connecting individual propositions with logical operators
logical operation
combines propositions using a particular composition rule
conjunction
/\, ‘p and q’, true if both p and q are true, false if one or both are false
truth table
shows truth value of a compound proposition for every possible combination of truth values for the variables
conjunction english examples
p and h, p but h, although p, h
disjunction
\/, ‘p or q’ ‘p \/ q’ true if either p or q or both are true, false if both are false
exclusive or (circle w/ plus)
evaluates to true when p is true and q is false, or vise versa
inclusive or
operates the same as disjunction
negation
reverses the truth value of the proposition
order of operations w/o parentheses
- negation, 2. conjunction, 3. disjunction, 4. exclusive or, 5. conditional operation, 6. biconditional operation
how many rows will be in a truth table?
n variables = 2^n rows
conditional operation
->, reads if p then q, false if p is true and q is false, otherwise, true
p -> q, what is proposition p called?
hypothesis
p -> q, what is proposition q called?
conclusion
conditional operation english expressions
if p, then q; if p, q; q if p; p implies q
converse of p -> q
q -> p
contrapositive of p -> q
negation(q) -> negation(p)
inverse of p -> q
negation(p) -> negation(q)
biconditional operation
p q, true when p and q have the same truth values and false when they do not
biconditional operation english expressions
p if and only if q, p is necessary and sufficient for q
iff
if and only if
tautology
when compound proposition is always true
contradiction
when compound proposition is always false
showing that compound proposition is tautology
show set of truth values for its individual propositions that cause the compound to be true
showing that compound proposition is contradiction
show set of truth values for its individual propositions that cause the compound to be false
logical equivalence
if they have the same truth value regardless of the truth values of their individual propositions (three lines)
de morgan’s law
negation(p \/ q) l.e negation(p) /\ negation(q)
