Transcript The If

Statements that are
Conditional with a
hypothesis and a
conclusion.
The If part of the
statement is the
Hypothesis, and the
Then part of the
statement is the
Conclusion.
A Champion is afraid to lose.
If you are a champion then
you are afraid to lose.
Examples
Statement
If-Then Form
Babies are small.
If a person is a baby,
then they are small.
A triangle has three
sides.
If a shape is a triangle,
then it has three sides.
Snakes are despised.
If an animal is a snake,
then it is despised.
Conditional
Statements have a
truth value, of true
or false. To prove
that a statement is
false it only takes
one counterexample
which shows that
the hypothesis is
true and the
conclusion is false.
If the sun is up then it is
morning.
If the sun is up then it can be in
the afternoon.
A Venn diagram
can be used to
illustrate
conditional
statements.
If you live in Chicago, then
you live in Illinois.
Residents of Illinois
Residents of
Chicago
Take the original
statement and
switch the
hypothesis and
the conclusion.
Conditional
If two points are on the same
line, then they are collinear.
Converse
If two points are collinear, then
they are on the same line.
More Examples
• Conditional
• If two lines intersect to form right
angles, then they are
perpendicular.
• Converse
• If two lines are perpendicular, then
they intersect to form right angles.
• Conditional
• If something is a cocker spaniel,
then it is a dog.
• Converse
• If something is a dog, then it is a
cocker spaniel.
Symbolic Form
p→q
q→p
You Read it
If p, then q.
If q, then p.
When a conditional and its converse are
true, you can combine them as a true
biconditional.
Conditional
If two angles have the same measure, then they are
congruent.
Converse
If two angles are congruent, then they have the same
measure.
Biconditional
Two angles have the same measure if and only if (iff ) the
angles are congruent.
p
q
Example:
Conditional
If an angle is a straight
angle, then its
measure is 180º.
Converse
If an angle has a
measure of 180º, then
it is a straight angle.
Biconditional
An angle is a straight
angle if and only if
(iff) its measure is
180º.
Symbolic Form:
You read it:
p→q
If p then q.
Symbolic Form:
q→p
Symbolic Form:
p
q
You read it:
If q then p.
You read it:
p if and only if q.