1. The FRAME
Essential details Essential details Essential details Essential details Essential details
Key Topic
is about . . .
So What? (What’s important to understand about this?)
Main Idea Main Idea Main Idea Main Idea Main Idea
Statement Biconditional
Statement
Converse Inverse Contrapositive
If p, then q.
p --> q
Ex: If an object is a
square, it is also a
polygon (true).
p if and
only if q.
p <--> q
If q, then p.
q --> p
Ex: If an object is a
polygon, it is also a
square (false).
If not p, then
not q.
~p --> ~q
Ex: If an object is not
a square, it is not a
polygon (false).
If not q, then
not p.
~q --> ~p
Ex: If an object is
not a polygon, it is
not a square (true).
True if converse
statement is
true.
True if original
statement is
true.
Logical Arguments
Ex: If alternate interior
angles are equal, then
the lines are parallel
(true).
Both the statement
and its converse
must be true.
Different forms of arguments used in logical reasoning.
The statement, converse, inverse and contrapositive are all related, and any one can be used
to find any one of the others. A biconditional statement is a type of statement that can be used
to write definitions, to solve equations and to state equivalences.
VA SOL G.1 a & b