logic Flashcards
One of the first mathematicians to make a serious study of
symbolic logic (1646 – 1716).
he tried to advance the study of logic from a merely
philosophical subject to a formal mathematical subject.
Gottfried Wilhelm Leibnitz
several
mathematicians have contributed to the
advancement of symbolic logic as a mathematical discipline.
Augustus De Morgan (1806 – 1871)
and George Boole (1815 – 1864)
To analyze an argument, we break it down into smaller pieces:
statements, logical connectives and quantifiers.
is a declarative sentence that is either true or false
statement
is a statement that conveys a single idea.
simple statement
consists of simple statements combined
using logical connectives like and, or, not, if…then.
compound statement
must have the opposite truth value
to the original statement
The negation of a statement
~
not
^, conjunction
and
disjunction, v
or
conditional, →
if..then
biconditional, ←→
if and only if
a simple statement is either true (T) or false(F)
- a compound statement depends on the truth
values of its simple statements and its connectives.
truth value
is a table that shows the truth value of a
compound statement for all possible truth values of its simple
statements.
truth table
all, every, each. Statement is true if the
claim is true for every object it is referring to.
Universal quantifier
some, there exists, for at least one.
Statement is true if the claim is true for atleast one object it is
referring to.
Existential quantifier
Shows truth value of a compound statement for all possible
truth values of the component statements
truth tables
If there are n component statements, then the truth table has
2n rows
is a statement that is always true.
tautology
is a statement that is always false.
self-contradiction
Two statements are ___ if they have the same truth
value for every possible situation, and we write p ≡ q
equivalent
for conditional, p is what??
antecedent
for conditional, q is what?
consequent
q → p.
if q, then p
converse
~p → ~q
if not p, then not q
inverse
~q → ~p
if not q, then not p
contrapositive
to determine whether logical
arguments are valid or invalid.
deductive reasoning
A logical argument is made up of ___ (assumptions,
statements assumed to be true) and a ____
premises and a conclusion
An argument is ___ if the fact that all the premises are true
forces the conclusion to be true.
valid
An argument that is not valid
invalid or fallacy
