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1
Chapter 2
Compound Statement
A statement formed by joining
two or more statements
Conclusion
In a conditional statement the
statement that immediately
follows the word then
Conditional Statement
a statement that can be written
in the form “If p, then q.” p is
the hypothesis and q is the
conclusion. Symbolically, if p,
then q can be written as p  q.
Conjunction
a compound statement formed
by joining two or more
statements with the word
“AND”.
Conjecture
A educated guess based on
known information
Converse
In the converse of a conditional
statement, the hypothesis and
conclusion are reversed. “If p,
then q.” becomes “If q, then p.”.
2
Chapter 2
Counterexample
An example used to show
that a given statement is not
always true
Deductive Reasoning
A system of reasoning that uses
facts, rules, definitions, or
properties to reach logical
conclusions
Disjunction
A compound statement formed
by joining two or more
statements with the word or
Hypothesis
In a conditional statement, the
statement that immediately
follows the word if
If-then statement
A compound statement of the
form “If A, then B”, where A and
B are statements
Inverse
The statement formed by
negating both the hypothesis
and conclusion of a conditional
statement
3
Chapter 2
Law of Contrapositive
in the contrapositive of a
conditional statement, the
hypothesis and conclusion are both
reversed and negated. “If p, then
q.” becomes “If not q, then not p.”.
The contrapositive has the same
truth value as the original
statement.
Law of Detachment
If p→q is a true conditional and
p is true, then q is also true
Law of Syllogism
If p→ q and q →r are true
conditionals, then p→ r is also
true
Logically equivalent
Statements that have the same
truth value
Negation
Has opposite meaning
Postulate
postulate, or axiom, indicates a
statement or assumption that is agreed
by everyone to be so obvious or selfevident that no proof is necessary; and
which can be used to prove other
statements or theorems. Neither
axioms nor postulates can be proved
(within a system) using more basic
statements.
4
Chapter 2
Proof
a valid argument in which all of
the premises are true
Statement
Any sentence that is either true
or false, but not both
Theorem
a statement or conjecture that
can be proven to be true based
on postulates, definitions, or
other proven theorems
Truth Table
A table used as a convenient
method for organizing the truth
values of statements
Truth Value
The truth of falsity of a
statement
Two-Column Proof
A formal proof that contains
statements and reasons
organized in two columns. Each
step is called a statement, and
the properties that justify each
step are call reasons
5
Chapter 2
Venn Diagram
show relationships between
different sets of data.
can represent conditional
statements. It is usually drawn as a
circle.
Every point IN the circle belongs to
that set.
Every point OUT of the circle does not.
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