2.1 Conditional Statements
Conditional Statement – a logical statement with
two parts.
P, the “if part”, hypothesis
Q, the “then part”, conclusion
If p, then q is symbolized as p -> q (p implies q).
Ex:
If you study hard, then you will get As.
If you live in Ridgewood, then you live in NJ.
If an angle is 28 degrees, then it is acute.
Rewrite into “If, then” form
• All fruits have seeds.
• Two angles that add up to 180 degrees are
supplementary.
• An even number is a number divisible by 2.
• 3x + 17 = 23, because x = 2.
• Only people who are 18 are allowed to vote.
• P=It is raining. Q =I must bring an umbrella.
• Today is Friday and tomorrow is Saturday.
Now go back and underline the hypothesis and
circle the conclusions.
Negation ~
The negation of a statement is the
opposite of the original statement.
Symbol: ~p
Words: not p
Examples: Find the negation of the statement.
1) This suit is black.
2) We are worthy.
Converse, Inverse and Contrapostive
Given Conditional Statement:
p->q
Converse: Switch hypothesis and conclusion.
q->p
Inverse: Negate hypothesis and conclusion.
~p->~q
Contrapositive: Switch and negate the
hypothesis and conclusion.
~q->~p
Counterexamples
A counterexample is a case that fits the
hypothesis but leads to a different conclusion.
You can prove a statement is false by finding a
counterexample.
Practice finding counterexamples.
1) If a number is prime, then it is odd.
2) If you live in Ridgewood, you go to RHS.
3) If a food is round, then it is pizza.
4) If a 3D figure lacks vertices, it is a sphere.
Conditional Statement: If you are a
guitar player, then you are a musician.
Converse: If you are a musician, then you are a
guitar player.
T or F
Inverse: If you are not a guitar player, then you
are not a musician.
T or F
Contrapositive. If you are not a musician, then
you are not a guitar player.
T or F
CONnie Mack was a SWITCH Hitter
Associate
CONverse
with
SWITCHING
the
hypothesis
and
conclusion
CONverses help me do a FLIP
The CONvict SWITCHES his clothes
once he escapes from jail.
N*Sync has a song NO strings attached
No Strings Attached
INverse think NOT
INdigo is not blue or not purple
If you are INdignant, you are
NEGATIVE
Contrapositive
• You SWITCH and NEGATE the hypothesis and
conclusion.
• It is like taking the converse and inverse at the
same time.
Fun Fact
• A conditional statement and its contrapositive
are either both true or false. They are
equivalent statements.
• A converse statement and an inverse
statement are also both true or false. They
are also equivalent statements.
• But (for example), a conditional may be true
and a converse may be false.
Guided Practice
Everyone will have to share, so make sure you
come up with something.
1) Write the definition of perpendicular lines as
a conditional statement. Is the converse
true?
2) Come up with your own conditional
statement. Then find the converse, inverse
and contrapositive.
3) Write true or false next to each of the four
statements you wrote in number 2.
Biconditional Statements
When a conditional statement and its converse are
true, you can write them as a single biconditional
statement linking the hypothesis and conclusion
with “if and only if”.
Words: p if and only if q
Symbol: p <-> q
Write a biconditional statement for your conditional
statement if both your conditional and converse
were true. If not, write one for perpendicular lines.