
In
logic, a biconditional is a compound
statement formed by combining two conditionals under
"and."
Biconditionals are true when
both
statements (facts) have the exact same truth value. 
A biconditional is read as
"[some fact] if and only if
[another fact]" and is true when
the truth values of both
facts are exactly the same
 BOTH TRUE or BOTH FALSE.
Biconditionals
are often
used to form definitions. 
Definition: A triangle is
isosceles if and only if the triangle has two congruent (equal) sides.
The "if and only if"
portion of the definition tells you that the statement is true when either
sentence (or fact) is the hypothesis. This means that both of the
statements below are true:
If a
triangle is isosceles, then the triangle has two
congruent (equal) sides.
(true)
If a
triangle has two congruent (equal) sides,
then the triangle is isosceles.
(true)
Mathematicians
often use symbols and tables to represent concepts in logic.
The use of these variables, symbols and tables creates a
shorthand method for discussing logical sentences.
Truth
table biconditional (if and only if):
(notice the
symbol used for "if and only if" in the table below)

A
truth
table is a pictorial representation of all of the possible
outcomes of the truth value of a compound sentence. Letters such
as _{}and _{}
are used to represent the facts (or sentences) within the
compound sentence. 

I
REMEMBER:
IF
AND ONLY IF is TRUE
when both facts are T
or both
facts are F.. 

