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Logic and Proofs

Definitions
o
proposition:
A statement that is true or false
o
propositional Variable: a
variable that represents a proposition
o
truth value:
true or false
o
¬
p (negation of p):
the proposition with the true value opposition to the truth value of p
o
logical operators:
operators used to combine propositions
o
compound proposition:
a proposition constructed by combining propositions using logical
operators
o
truth table:
a table displaying the truth values of propositions
o
q
p
∨
(disjunction of p and q):
the proposition “p or q,” which is true if and only if at least one of
p and q is true
o
q
p
∧
(conjunction of p and q):
the proposition “p and q,” which is true if and only if both p and q
are true
o
q
p
⊕
(exclusive or of p and q): the
proposition “p XOR q,” which is true when exactly one of p
and q are true
o
q
p
→
(p implies q):
the proposition “if p, then q,” which is false if and only if p is true and q is
false
o
converse of
q
p
→
:
the conditional statement
p
q
→
o
contrapositive of
q
p
→
:
the conditional statement
p
q
¬
→
¬
o
inverse of
q
p
→
:
the conditional statement
q
p
¬
→
¬
o
q
p
↔
(biconditional):
the proposition “p if and only if q,” which is true if and only if p and q
have the same truth value
o
bit:
either a 0 or a 1
o
boolean variable:
a variable that has a value of 0 or 1
o
bit operation:
an operation of a bit or bits
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This note was uploaded on 04/14/2008 for the course CS 2800 taught by Professor Selman during the Fall '07 term at Cornell University (Engineering School).
 Fall '07
 SELMAN

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